Multiply <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mi>a</mi><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mi>a</mi></msqrt><mo>-</mo><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>-</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mi>a</mi><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mi>a</mi></msqrt><mo>-</mo><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>-</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mstyle></math> .

Expand the denominator using the FOIL method.

Simplify.

Apply the distributive property.

Combine using the product rule for radicals.

Raise <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Rewrite using the commutative property of multiplication.

Simplify each term.

Pull terms out from under the radical.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><msqrt><mi>a</mi><mi>b</mi></msqrt><msqrt><mi>b</mi></msqrt></mstyle></math> .

Combine using the product rule for radicals.

Raise <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Reorder <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> and <math><mstyle displaystyle="true"><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><msqrt><mi>b</mi></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><msqrt><mi>a</mi></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><mi>a</mi><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>-</mo><mi>b</mi><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Move <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><mi>a</mi><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mi>b</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow><mo>+</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mrow><mo>(</mo><mo>-</mo><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow></mstyle></math> .

Do you know how to Evaluate ( square root of ab)/( square root of a+ square root of b)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | one billion eight hundred ninety-two million one hundred fifty-three thousand five hundred fifteen |
---|

- 1892153515 has 8 divisors, whose sum is
**2594953440** - The reverse of 1892153515 is
**5153512981** - Previous prime number is
**7**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 40
- Digital Root 4

Name | eight hundred twenty-five million nine hundred sixty thousand six hundred seventy-three |
---|

- 825960673 has 4 divisors, whose sum is
**835241220** - The reverse of 825960673 is
**376069528** - Previous prime number is
**89**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 46
- Digital Root 1

Name | one billion eight hundred twenty-eight million twenty thousand four hundred forty-four |
---|

- 1828020444 has 64 divisors, whose sum is
**5627653632** - The reverse of 1828020444 is
**4440208281** - Previous prime number is
**211**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 33
- Digital Root 6