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

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

Step-by-step 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)

3 x^3 * y^4*√ (5x)

Step-by-step 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)