What is the simplest form of the radical expression : sqrt(72x ^ 5 * y ^ 4)
pls and thx!
+30 \(6x^2y^2\sqrt2x\)
Simplify the radical by breaking the radicand up into a product of known factors
+298 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
Add parentheses.
√(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.
+30 More detailed response:
\(\sqrt{72x^5y^4}\)
=\(\sqrt{72}\sqrt{x^5}\sqrt{y^4}\)
=\(6\sqrt{2}\sqrt{x^5}\sqrt{y^4}\)
=\(6\sqrt{2}\sqrt{x^4x^1}\sqrt{y^4}\)
=\(6\sqrt{2}\sqrt{\left(x^2\right)^2}\sqrt{x^1}\sqrt{y^4}\)
=\(6\sqrt{2}x^2\sqrt{x^1}\sqrt{\left(y^2\right)^2}\)
=\(6\sqrt{2}x^2y^2\sqrt{x}\)
=\(6\sqrt{2}x^2y^2\sqrt{x}\)
=\(6x^2y^2\sqrt2x\)
