Simplify the Radical Expression square root of -9+ square root of -25- square root of -5

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>9</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt><mo>⋅</mo><msqrt><mn>9</mn></msqrt></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

The absolute value is the distance between a number and zero. The distance between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>25</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>25</mn><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>25</mn><mo>)</mo></mrow></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt><mo>⋅</mo><msqrt><mn>25</mn></msqrt></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

The absolute value is the distance between a number and zero. The distance between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>5</mn><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>5</mn><mo>)</mo></mrow></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt><mo>⋅</mo><msqrt><mn>5</mn></msqrt></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>3</mn><mi>i</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>5</mn><mi>i</mi></mstyle></math> .

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