Solve and show workings
3√/9 *27√
It's supose to be the square root of 3 over 9 time the quare root of 27.
i know the answer is 1 however i don't know how to get that answer. Any help would be appriciated. Thanks
(1/9) sqrt 3 * sqrt 27 ?
note 27 = 3^3 so sqrt 27 = 3^1.5
3^-2 * 3^.5 * 3^(1.5)
= 3^-2 * 3^+2
= 3^0 = 1
thankyou so much!
To solve the expression (3√3/9) * 27√:
Step 1: Simplify the square roots individually.
The square root of 3 can be written as √3.
The square root of 27 can be written as √(3 * 9) = √3 * √9 = √3 * 3 = 3√3.
Now, the expression becomes (3√3/9) * 3√3.
Step 2: Simplify the fraction.
To simplify the fraction, divide both the numerator and the denominator by the greatest common divisor, which is 3 in this case.
(3√3/9) reduces to (√3/3).
So, the expression simplifies to (√3/3) * 3√3.
Step 3: Multiply the terms.
When multiplying square roots, you can multiply the numbers outside the square root as well as the numbers inside the square root.
(√3/3) * 3√3 = (√3/3) * (3 * √3) = (√3/3) * 3 * √3 = (√3/3) * 3√3 * 1 = (√3 * √3/3) * 3 * 1 = (√3 * √3/3) * 3 = (3 * 3 * √3 * √3)/3 = (9 * 3)/3 * (√3 * √3) = 27/3 * 3 = 27/1 = 27.
So, the final answer is 27.