How do you simplify the square root of 458?

Question

How do you simplify the square root of 458?

1 Answer

Impact of this question

7339 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-04-23T08:27:45

This can be solved easily using a Calculator . We get the answer as $\approx 21.400935$ $color(green)(approx 21.400935$

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

$\sqrt{458} = \sqrt{2 \cdot 229} = \sqrt{2} \cdot \sqrt{229}$ $sqrt458 = sqrt(2*229) = sqrt 2 * sqrt 229$

We know that $\sqrt{2} \approx 1.4142$ $sqrt 2 approx 1.4142$

To find the $\sqrt{229}$ $color(blue)(sqrt229$ , we can use the following formula:

$\sqrt{N o n - P e r f e c t - S q u a r e} \approx \sqrt{N e a r e s t - P e r f e c t - S q u a r e} + \frac{D e v i a t i o n}{2 \cdot \sqrt{N e a r e s t - P e r f e c t - S q u a r e}}$ $sqrt(Non-Perfect-Square) approx sqrt(Nearest-Perfect-Square) + (Deviation)/(2*sqrt(Nearest-Perfect-Square))$

The nearest perfect square to 229 is $225$ $225$ . And the deviation is $229 - 225 = 4$ $229 - 225 = 4$

$\sqrt{229} \approx \sqrt{225} + \frac{4}{2 \cdot \sqrt{225}}$ $sqrt 229 approx sqrt 225 + (4)/(2*sqrt225)$

$\approx 15 + (\frac{4}{30}) \approx 15.133$ $approx 15 + (4/30) approx color(blue)(15.133$

Hence we get $\sqrt{458} \approx 1.4142 \cdot 15.133 \approx 21.4015$ $sqrt458 approx 1.4142 * 15.133 approx color(green)(21.4015$

Science

Math

Humanities

... and beyond

How do you simplify the square root of 458?

1 Answer

Related questions

Impact of this question