Rewrite <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msqrt><mi>x</mi></msqrt><mo>+</mo><msqrt><mn>2</mn></msqrt><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mrow><mo>(</mo><msqrt><mi>x</mi></msqrt><mo>+</mo><msqrt><mn>2</mn></msqrt><mo>)</mo></mrow><mrow><mo>(</mo><msqrt><mi>x</mi></msqrt><mo>+</mo><msqrt><mn>2</mn></msqrt><mo>)</mo></mrow></mstyle></math> .

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify each term.

Multiply <math><mstyle displaystyle="true"><msqrt><mi>x</mi></msqrt><msqrt><mi>x</mi></msqrt></mstyle></math> .

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

Raise <math><mstyle displaystyle="true"><msqrt><mi>x</mi></msqrt></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 <math><mstyle displaystyle="true"><msup><mrow><msqrt><mi>x</mi></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mi>x</mi></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>x</mi></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify.

Combine using the product rule for radicals.

Combine using the product rule for radicals.

Combine using the product rule for radicals.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

Add <math><mstyle displaystyle="true"><msqrt><mi>x</mi><mo>⋅</mo><mn>2</mn></msqrt></mstyle></math> and <math><mstyle displaystyle="true"><msqrt><mn>2</mn><mi>x</mi></msqrt></mstyle></math> .

Reorder <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><msqrt><mn>2</mn><mo>⋅</mo><mi>x</mi></msqrt></mstyle></math> and <math><mstyle displaystyle="true"><msqrt><mn>2</mn><mi>x</mi></msqrt></mstyle></math> .

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