What is the square root of 464?

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What is the square root of 464?

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Answer 1 · 2015-10-16T21:24:35

$4 \sqrt{29}$ $4sqrt(29)$

Explanation:

This square root isn't the square root of a perfect square. The only thing we can do is to simplify the expression. First let's try dividing by two until we can't anymore:
$\sqrt{464} = \sqrt{2 \cdot 232} = \sqrt{2 \cdot 2 \cdot 116} = \sqrt{2 \cdot 2 \cdot 2 \cdot 58} = \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 29} = \sqrt{16 \cdot 29}$ $sqrt(464)=sqrt(2*232)=sqrt(2*2*116)=sqrt(2*2*2*58)=sqrt(2*2*2*2*29)=sqrt(16*29)$

At this point, we can't divide $29$ $29$ anymore, because it is a prime number. You can split this expression in:
$\sqrt{16} \cdot \sqrt{29} = 4 \sqrt{29}$ $sqrt(16)*sqrt(29) = 4sqrt(29)$

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What is the square root of 464?

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