Can someone show me step by step examples of simplifying
3√5/64
thank you
If you mean √5 / 64 there is nothing left to do.
If you meant √(5/64), you can use the fact that √64=8 to reduce the fraction to 3√5 / 8
Absolutely! I will guide you step by step on how to simplify the expression 3√5/64.
Step 1: Start by simplifying the denominator. In this case, the denominator is 64. We can rewrite 64 as 4^3 since it is equal to 4 × 4 × 4.
Step 2: Simplify the cube root in the numerator. We have 3√5. Since there is no perfect cube factor for 5, we cannot simplify it further.
Step 3: Simplify the cube root in the denominator. Since the denominator is 4^3, we can simplify it as the cube root of 4 cubed, which is given by 4^(3/3) = 4^1 = 4.
Step 4: Now we have 3√5/4. The expression is already simplified, but if you want to rationalize the denominator, which means eliminating the radical in the denominator, you can proceed to the next step.
Step 5: To rationalize the denominator, multiply the expression by a suitable form of 1 that eliminates the cube root from the denominator. In this case, we multiply by the cube root of 4^2, which is 4^(2/3).
(3√5/4) * (4^(2/3) / 4^(2/3))
Step 6: Multiply the numerators and denominators together.
(3√5 * 4^(2/3)) / (4 * 4^(2/3))
Step 7: Simplify the numerator.
3√(5 * 4^(2/3)) / (4 * 4^(2/3))
Step 8: Simplify the denominator.
3√(5 * 4^(2/3)) / (4 * (4^(1/3))^2)
3√(5 * 4^(2/3)) / (4 * 4^(2/3))
Step 9: Combine like terms.
3√(5 * 4^(2/3)) / 4^(5/3)
And that's the final simplified form of the expression 3√5/64.