10√3/3√15
To simplify the expression 10√3/3√15, we can first simplify the square roots in both the numerator and denominator.
The square root of 3 cannot be simplified further.
The square root of 15 can be simplified as follows:
√15 = √(3 * 5) = √3 * √5
Now our expression becomes:
10√3 / 3(√3 * √5)
Next, we can simplify the expression further by canceling out like terms.
The √3 in the numerator cancels out with one of the √3s in the denominator.
Our simplified expression then becomes:
10 / 3√5
To simplify the expression 10√3 / 3√15, we can follow these steps:
Step 1: Simplify the numerator (the top part of the fraction):
10√3 = √(10^2) * √3 = √(100 * 3) = √300
Step 2: Simplify the denominator (the bottom part of the fraction):
3√15 = √(3^2) * √15 = √(9 * 15) = √135
Step 3: Simplify the square roots:
√300 = √(3 * 100) = √3 * √100 = √3 * 10 = 10√3
√135 = √(5 * 27) = √5 * √27 = √5 * 3√3
Step 4: Combine the simplified numerator and denominator:
10√3 / 3√15 = (10√3) / (3√15) = (10√3) / (3√5 * 3√3) = (10√3) / (9√5)
Therefore, the simplified expression is (10√3) / (9√5).
To simplify the expression 10√3/3√15, we need to rationalize the denominators. Rationalizing the denominator means getting rid of any square roots in the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
First, we have the expression 10√3/3√15. To rationalize the denominator, we need to multiply both the numerator and denominator by the conjugate of 3√15, which is the expression formed by changing the sign of the square root, i.e., -3√15.
So, we have:
10√3/3√15 * -3√15/-3√15
Expanding this expression, we get:
(-30√45)/(-9√225)
Now, we simplify the expression inside the square roots:
√45 = √(9 * 5) = √9 * √ 5 = 3√5
√225 = 15
Substituting these values back into the expression, we get:
(-30 * 3√5)/(-9 * 15)
Simplifying further, we have:
-90√5 / -135
To simplify the expression, we can cancel out common factors:
-90/(-135) = 90/135 = 2/3
Therefore, 10√3/3√15 simplifies to 2/3.