Question

Rewrite the radical by extracting all possible roots and write your answer in radical form 75x4y7−−−−−−√

Answer 1

`√(75x^4y^7) = 5x^2y^3√(3y)`

Explanation:

Given

`\sqrt{75x^4y^7`

Required

Rewrite

Express 75 as 25 * 3

`√(75x^4y^7) = √(25 * 3x^4y^7)`

Split

`√(75x^4y^7) = √(25) * √(3x^4y^7)`

This gives:

`√(75x^4y^7) = 5 * √(3x^4y^7)`

Express y^7 as y^6 * y

`√(75x^4y^7) = 5 * √(3*x^4 * y^6 * y)`

Split

`√(75x^4y^7) = 5 * √(3) *√(x^4) * √(y^6) * √(y)`

Express square roots as exponents

`√(75x^4y^7) = 5 * √(3) * x^{(4 * (1)/(2))} * y^{(6* (1)/(2))} * √(y)`

`√(75x^4y^7) = 5 * √(3) * x^2 * y^3 * √(y)`

Rewrite the factors

`√(75x^4y^7) = 5 * x^2 * y^3* √(3) * √(y)`

`√(75x^4y^7) = 5x^2y^3* √(3) * √(y)`

Combine roots

`√(75x^4y^7) = 5x^2y^3* √(3y)`

`√(75x^4y^7) = 5x^2y^3√(3y)`