SIMPLIFY:
ROOT 0F 7 * ROOT OF 14
SIMPLIFY:
ROOT OF 1/5
EVALUATE, IF POSSIBLE:
ROOT OF 9/16
(I GOT 3/4 BUT I WAS NOT SURE IF THAT WAS CORRECT OR NOT)
SIMPLIFY. ASSUME X REPRESENTS A POSITIVE NUMBER:
ROOT OF 45X^4
ROOT 0F 7 * ROOT OF 14 = sqrt 7 * sqrt 7 * sqrt 2 = 7 sqrt 2
ROOT OF 1/5 = 1 /(sqrt 5)
ROOT OF 9/16 = sqrt 9/sqrt 16 = 3/4
sqrt(45X^4) = sqrt 45 * X^2
To solve these problems, we'll use some basic rules of square roots.
1. ROOT OF 7 * ROOT OF 14:
We start by simplifying each square root individually:
ROOT OF 7 can't be simplified further, so it remains as sqrt(7).
ROOT OF 14 can be simplified as sqrt(7) * sqrt(2), since 14 can be broken down into the product of 7 and 2.
Finally, we multiply the simplified square roots together: sqrt(7) * sqrt(7) * sqrt(2) = 7 * sqrt(2).
Therefore, the simplified expression is 7 sqrt(2).
2. ROOT OF 1/5:
To simplify, we write it as a fraction:
ROOT OF 1/5 = 1 / (sqrt(5)).
This is because a square root in the denominator moves to the numerator.
So, the simplified expression is 1 / sqrt(5).
3. ROOT OF 9/16:
We start by simplifying the numerator and denominator separately:
The square root of 9 is 3, and the square root of 16 is 4.
So we have sqrt(9) / sqrt(16) = 3/4.
Therefore, the simplified expression is 3/4.
4. ROOT OF 45X^4:
We can break down 45 and X^4 separately:
sqrt(45) * sqrt(X^4).
The square root of 45 can be simplified as sqrt(9) * sqrt(5), since 45 = 9 * 5.
The square root of X^4 simplifies to X^2.
Finally, we multiply the simplified square roots together: sqrt(9) * sqrt(5) * X^2 = 3 * sqrt(5) * X^2.
So, the simplified expression is 3 sqrt(5) X^2.
Please note that these answers are based on the assumption that X represents a positive number, as specified in the problem statement.
= sqrt (9*5) * X^2
= 3 sqrt(5) * X^2