Question

Estimate 456 by finding square root of a perfect square

Answer 1

Square root of 456 definition

The square root of 456 in mathematical form is written with the radical sign like this √456. We call this the square root of 456 in radical form. The square root of 456 is a quantity (q) that when multiplied by itself will equal 456.

√456 = q × q = q2

Is 456 a perfect square?

456 is a perfect square if the square root of 456 equals a whole number. As we have calculated further down on this page, the square root of 456 is not a whole number.

456 is not a perfect square.

Can the square root of 456 be simplified?

You can simplify 456 if you can make 456 inside the radical smaller. We call this process "to simplify a surd". The square root of 456 can be simplified.

√456 = 2√114

Answer 2

Step-by-step explanation:

$456 = 2 \times 2 \times 2 \times 3 \times 19$

$= {2}^{3} \times {3}^{} \times 19$

$\sqrt{456} = 2 \sqrt{114}$

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