What is the simplification of sqrt((18x^5y^4)/(49xz^3))18x5y449xz3?

1 Answer
Jul 31, 2016

(3x^2y^2sqrt(2z))/(7z^2)3x2y22z7z2

Explanation:

color(blue)("General comment")General comment

Any values that are squares can be taken outside the square root. So for example if you had sqrt(2^2xx3)22×3 you could write this as
2sqrt(3)23. Or if you had sqrt(2^4xx3)24×3 you could write 2^2sqrt(3)223

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color(blue)("Answering the question")Answering the question

Write as sqrt(2xx3^2xx x xx x^4xx y^4)/(sqrt(7^2 xz xx z^2)2×32×x×x4×y472xz×z2 giving:

(3x^2y^2sqrt(2x))/(7zsqrt(xz)) 3x2y22x7zxz

Write as:" "(3x^2y^2sqrt2cancel(sqrtx))/(7zsqrtz cancel(sqrtx))

Multiply by 1 but in the form of 1=sqrtz/sqrtz giving

(3x^2y^2)/(7z)xxsqrt(2)/sqrt(z) xx sqrtz/sqrtz

(3x^2y^2sqrt(2z))/(7z^2)