# How do you simplify sqrt87?

##### 1 Answer
Apr 22, 2015

This can be solved easily using a Calculator . We get the answer as color(green)(approx 9.32738

But if we are expected to do it without a calculator , here's how it can be done.

$\sqrt{87} = \sqrt{3 \cdot 29} = \sqrt{3} \cdot \sqrt{29}$

We know that $\sqrt{3} \approx 1.732$

To find the color(blue)(sqrt29, we can use the following formula:

$\sqrt{N o n - P e r f e c t - S q u a r e} \approx \sqrt{N e a r e s t - P e r f e c t - S q u a r e} + \frac{D e v i a t i o n}{2 \cdot \sqrt{N e a r e s t - P e r f e c t - S q u a r e}}$

The nearest perfect square to 29 is $25$. And the deviation is $29 - 25 = 4$

$\sqrt{29} \approx \sqrt{25} + \frac{4}{2 \cdot \sqrt{25}}$

 approx 5 + (4/10) approx color(blue)(5.4

Hence we get sqrt87 approx 1.732 * 5.4 approx color(green)(9.353