Carly Pehrson

Posted on Saturday, 31 May, 2003 - 07:19 pm:

I'm doing an equation that comes down to a number squared equals the square root of a number that is not a perfect square. If I find the square root of both sides, will a number equal the fourth root of the number that is not a perfect square? Basically, what is the square root of a square root? Is the square root of a square root a fourth root?

David Loeffler

Posted on Saturday, 31 May, 2003 - 07:24 pm:

Yes. The square root of (the square root of

x

) is the fourth root of

x

Suppose $y = \sqrt{\sqrt{x}}$

then $y^{2} = \sqrt{x}$

$(y^{2})^{2} = x$

But $(y^{2})^{2} = y^{4}$ , so $y^{4} = x$ , so $y = \sqrt[4]{x}$ .

David

Matthew Buckley

Posted on Saturday, 31 May, 2003 - 07:24 pm:

Yes

Carly Pehrson

Posted on Saturday, 31 May, 2003 - 08:47 pm:

Thank you. You put it in much simpler terms than the websites I visited. They all left me uncertain. Last time I had a question about math, it was answered here at NRICH, too. Thanks.

Richard Crockford

Posted on Sunday, 01 June, 2003 - 10:21 am:

If you think of

\sqrt{\sqrt{x}}

this is the same as

(x^{0.5}

which, by multiplying the indices gives

x^{0.25}

, the fourth root of

x