How do you simplify sqrt(9x^4)√9x4?

1 Answer
Tony B
Apr 29, 2016

3x^23x2

Explanation:

9=3^2" and "x^4 = (x^2)^29=32 and x4=(x2)2

Multiply any number by 1 and you do not change that number's value. I am including the value 1 just to demonstrate a process.

So write as:" sqrt(1xx3^2xx(x^2)^2)√1×32×(x2)2

Taking all squared values outside the square root removing the square. For (x^2)^2(x2)2 you remove the outer square.

3xx x^2xxsqrt(1)3×x2×√1

But sqrt(1) = 1√1=1 so we have

3xx x^2xx1" "=" "3x^23×x2×1 = 3x2
'~~~~~~~~~~~~~~~~~~~~~~~~~~
This trick of multiply by 1 is used in higher maths when you have
sqrt(-4)->sqrt(-1xx4)->2sqrt(-1)√−4→√−1×4→2√−1

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