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What  is the simplest  form  of the radical  expression : sqrt(72x ^ 5 * y ^ 4)

pls and thx!

Dec 16, 2019

#1
0

$$6x^2y^2\sqrt2x$$

Simplify the radical by breaking the radicand up into a product of known factors

Dec 16, 2019
#2
+4

Rewrite 72x5⋅y472x5⋅y4 as (6x^2⋅y^2)^2⋅(2x)

Factor 3636 out of 7272.

√36(2)x5⋅y436(2)x5⋅y4

Rewrite 3636 as 6262.

√62⋅2x^5⋅y^4 as 62⋅2x5⋅y4

Factor out x4x4.

√62⋅2(x4x)⋅y462⋅2(x4x)⋅y4

Rewrite x4x4 as (x2)2(x2)2.

√62⋅2((x2)2x)⋅y462⋅2((x2)2x)⋅y4

Rewrite y4y4 as (y2)2(y2)2.

√62⋅2((x2)2x)⋅(y2)262⋅2((x2)2x)⋅(y2)2

Move xx.

√62⋅2((x2)2)⋅(y2)2x62⋅2((x2)2)⋅(y2)2x

Move 22.

√(62((x2)2))⋅(y2)2⋅2x(62((x2)2))⋅(y2)2⋅2x

Rewrite (62((x2)2))⋅(y2)2(62((x2)2))⋅(y2)2 as (6x2⋅y2)2(6x2⋅y2)2.

√(6x2⋅y2)2⋅2x(6x2⋅y2)2⋅2x

√(6x2⋅y2)2⋅(2x)(6x2⋅y2)2⋅(2x)

Pull terms out from under the radical.

∣∣6x2⋅y2∣∣√2x|6x2⋅y2|2x

Remove non-negative terms from the absolute value.

6x^2y^2√2x

sorry that it might be unclear, but the answer is above.

Dec 16, 2019
edited by tomsun  Dec 16, 2019
#3
+2

nice!

Dec 16, 2019
#4
0

More detailed response:

$$\sqrt{72x^5y^4}$$

=$$\sqrt{72}\sqrt{x^5}\sqrt{y^4}$$

=$$6\sqrt{2}\sqrt{x^5}\sqrt{y^4}$$

=$$6\sqrt{2}\sqrt{x^4x^1}\sqrt{y^4}$$

=$$6\sqrt{2}\sqrt{\left(x^2\right)^2}\sqrt{x^1}\sqrt{y^4}$$

=$$6\sqrt{2}x^2\sqrt{x^1}\sqrt{\left(y^2\right)^2}$$

=$$6\sqrt{2}x^2y^2\sqrt{x}$$

=$$6\sqrt{2}x^2y^2\sqrt{x}$$

=$$6x^2y^2\sqrt2x$$

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Dec 16, 2019