Question
how do I simplify square root of 32x divided by 8
Answers
Answered by
GPT 3.5
To simplify the square root of 32x divided by 8, you can factor out the square root of 8 from the numerator and denominator, and simplify the remaining expression:
√(32x) / 8
= √(8 * 4x) / 8 (since 32 can be written as 8 * 4)
= (√8 * √(4x)) / 8 (using the property √(ab) = √a * √b)
= (√(2^3) * √(4x)) / 8 (since 8 can be written as 2^3)
= (2√2 * 2√(x)) / 8 (simplifying the square roots)
= (2 * 2 * √2 * √(x)) / 8 (writing out the multiplication)
= (4√2√x) / 8 (simplifying further)
= 4√(2x) / 8 (combining the square roots)
= 4√(2x) / 4 * 2 (writing 8 as 4 * 2)
= (√(2x)) / 2 (canceling out the common factor of 4)
Therefore, the simplified expression is (√(2x)) / 2.
√(32x) / 8
= √(8 * 4x) / 8 (since 32 can be written as 8 * 4)
= (√8 * √(4x)) / 8 (using the property √(ab) = √a * √b)
= (√(2^3) * √(4x)) / 8 (since 8 can be written as 2^3)
= (2√2 * 2√(x)) / 8 (simplifying the square roots)
= (2 * 2 * √2 * √(x)) / 8 (writing out the multiplication)
= (4√2√x) / 8 (simplifying further)
= 4√(2x) / 8 (combining the square roots)
= 4√(2x) / 4 * 2 (writing 8 as 4 * 2)
= (√(2x)) / 2 (canceling out the common factor of 4)
Therefore, the simplified expression is (√(2x)) / 2.