Question

find the value of √576/2025​

Answer 1

Step-by-step explanation:

$\sqrt{\frac{576}{2025} } =\frac{\sqrt{576} }{\sqrt{2025} } =\frac{24}{45} =\frac{8}{15}$

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Answer 2

SOLUTION

TO DETERMINE

The value of

$\displaystyle \sf{ \sqrt{ \frac{576}{2025} } }$

EVALUATION

Here we have to find the value of

$\displaystyle \sf{ \sqrt{ \frac{576}{2025} } }$

Now

$\displaystyle \sf{ \sqrt{ \frac{576}{2025} } }$

$\displaystyle \sf{ = \sqrt{ \frac{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 }{5 \times 5 \times 3 \times 3 \times 3 \times 3} } }$

$\displaystyle \sf{ = \sqrt{ \frac{ {2}^{2} \times {2}^{2} \times {2}^{2} \times {3}^{2} }{ {5}^{2} \times {3}^{2} \times {3}^{2} } } }$

$\displaystyle \sf{ =\frac{ 2 \times 2 \times 2 \times 3 }{ 5 \times 3 \times 3}}$

$\displaystyle \sf{ =\frac{ 24 }{ 45}}$

$\displaystyle \sf{ =\frac{ 8 }{15}}$

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