How do you simplify $sqrt87$ ?

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Answer 1 · 2015-04-22T10:17:33

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.

$sqrt87 = sqrt(3*29) = sqrt 3 * sqrt 29$

We know that $sqrt 3 approx 1.732$

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

$sqrt(Non-Perfect-Square) approx sqrt(Nearest-Perfect-Square) + (Deviation)/(2*sqrt(Nearest-Perfect-Square))$

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

$sqrt 29 approx sqrt 25 + (4)/(2*sqrt25)$

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

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

How do you simplify sqrt87sqrt87?