Week 17 MCQ Madness

Answer explanation

To simplify \(\sqrt[]{36x^4}\), we can break it down as \(\sqrt[]{36} \times \sqrt[]{x^4} = 6 \times x^2 = 6x^2\), so the correct choice is \(6x^2\).

Answer explanation

To simplify the cube root of 8x^3, we can rewrite it as the cube root of (2x)^3, which equals 2x.

Answer explanation

To simplify \(\sqrt[]{49y^6}\), we can break down the square root into \(\sqrt[]{49} \times \sqrt[]{y^6} = 7y^3\), so the correct answer is \(7y^3\).

Answer explanation

To simplify, we can rewrite the expression as \(\sqrt[4]{81x^8} = \sqrt[4]{(3^4)(x^2)^4} = 3x^2\), so the correct choice is \(3x^2\).

Answer explanation

The correct answer is 4xy^2. To simplify, take the square root of 16 which is 4, and the square root of x^2 which is x, and y^4 which simplifies to y^2. Therefore, the answer is 4xy^2.

Answer explanation

To simplify the cube root of 27x^6y^3, we find the cube root of each term: 3x^2y. Therefore, the correct choice is 3x^2y.

Answer explanation

To simplify the square root of 64z^8, we can break down 64 into 8 * 8 and z^8 into z^4 * z^4. This gives us 8z^4 as the simplified form.

Answer explanation

To simplify the fourth root of 256x^12, we find the fourth root of 256 (which is 4) and divide the exponent by 4 to get x^3. Therefore, the answer is 4x^3.

Answer explanation

To simplify the square root of 25x^2y^8, we take the square root of 25 (which is 5) and half the exponents, resulting in 5xy^4.

Answer explanation

To simplify the cube root of 125x^9y^6, we find the cube root of each factor: 125 = 5^3, x^9 = x^3, and y^6 = y^2. Therefore, the simplified form is 5x^3y^2.