Radicals Rock=R^2..Ooops those are exponents

Algebra Level pending

sqrtroot96x^2y^4z

5sqrtrootxyz 3xy^2sqrtrootpz 96sqrtrootxyz 4xy^2sqrtroot6z

Abdullah Warriach by abdullah warriach , 20, USA

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2 solutions

Saurabh Mallik
Feb 18, 2016

Question is square root of 96 x 2 y 4 z 96x^{2}y^{4}z

96 x 2 y 4 z = 16 × 6 x 2 ( y 2 ) 2 z \sqrt{96x^{2}y^{4}z} = \sqrt{16\times6x^{2}(y^{2})^{2}z}

= 4 2 × 6 x 2 ( y 2 ) 2 z =\sqrt{4^{2}\times6x^{2}(y^{2})^{2}z}

= 4 x y 2 6 z = 4xy^{2}\sqrt{6z}

So, the answer is: 96 x 2 y 4 z = 4 x y 2 6 z \boxed{\sqrt{96x^{2}y^{4}z}=4xy^{2}\sqrt{6z}}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

So first we find two numbers that multiply to 96 and one of them must be a perfect square..I chose 16 & 6 ..16 can be changed to 4 so that can come outside but 6 stays in the sqrtroot. Radicals are about pairs so we bring out x. Since x is raised to power of 2 there is only one left on the outside. In same way y=2 on the outside. since there is only 1 z it stays inside with the 6. P.S. I KNOW I DIDN"T EXPLAIN IT VERY WELL BUT TRIED MY BEST...

0 Helpful 0 Interesting 0 Brilliant 0 Confused

You could have used the L a t e x Latex for better representation.

Question is square root of 96 x 2 y 4 z 96x^{2}y^{4}z

96 x 2 y 4 z = 16 × 6 x 2 ( y 2 ) 2 z \sqrt{96x^{2}y^{4}z} = \sqrt{16\times6x^{2}(y^{2})^{2}z}

= 4 2 × 6 x 2 ( y 2 ) 2 z =\sqrt{4^{2}\times6x^{2}(y^{2})^{2}z}

= 4 x y 2 6 z = 4xy^{2}\sqrt{6z}

So, the answer is: 96 x 2 y 4 z = 4 x y 2 6 z \boxed{\sqrt{96x^{2}y^{4}z}=4xy^{2}\sqrt{6z}}

Saurabh Mallik - 5 years, 3 months ago

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