Linear Algebra Examples

$\sqrt{\frac{192}{121}}$

Step 1

Rewrite

$\sqrt{\frac{192}{121}}$ as

$\frac{\sqrt{192}}{\sqrt{121}}$ .

$\frac{\sqrt{192}}{\sqrt{121}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite

$192$ as

$8^{2} \cdot 3$ .

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Step 2.1.1

Factor

$64$ out of

$192$ .

$\frac{\sqrt{64 (3)}}{\sqrt{121}}$

Step 2.1.2

Rewrite

$64$ as

$8^{2}$ .

$\frac{\sqrt{8^{2} \cdot 3}}{\sqrt{121}}$

Step 2.2

Pull terms out from under the radical.

$\frac{8 \sqrt{3}}{\sqrt{121}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite

$121$ as

$11^{2}$ .

$\frac{8 \sqrt{3}}{\sqrt{11^{2}}}$

Step 3.2

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

$\frac{8 \sqrt{3}}{11}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{8 \sqrt{3}}{11}$

Decimal Form:

$1.25967331 \dots$