Question

Simplify. Assume that all variables represent positive real numbers. sqrt[45][x]^[7][y]^[8]

Answer 1

3 x^3 * y^4*√(5x)

Explanation:

Factor

45: 3 * 3 * 5

y^8 = y * y * y * y *y * y * y * y

x^7 = x *x *x *x *x *x *x

Now underline every pair.

Rule: for every pair, take 1 outside the square root sign and throw the other one away. If any of the bases are left over, leave them under the square root sign.

3 * y * y * y * y * x * x * x * √ (5 * y)

Answer: 3 x^3 * y^4*√(5x)

Answer 2

3 x^3 y^4 sqrt(5x)

Explanation:

sqrt(45x^7y^8)

We know that sqrt(ab) = sqrt(a)sqrt(b)

sqrt(45)sqrt(x^7) sqrt(y^8)

sqrt(9*5) sqrt(x^2 *x^2 * x^2* x) sqrt(y^2 *y^2 *y^2 *y^2)

We know that sqrt(ab) = sqrt(a)sqrt(b)

sqrt(9)sqrt(5) sqrt(x^2)sqrt(x^2) sqrt(x^2) sqrt(x) sqrt(y^2)sqrt(y^2)sqrt(y^2)sqrt(y^2)

3 sqrt(5) x*x*x sqrt(x) y*y*y*y

3 x^3 y^4 sqrt(5)sqrt(x)

3 x^3 y^4 sqrt(5x)