Simplify √7/(3+7)² giving your answer in surd form with a rational denominator
To simplify √7/(3+7)², we first need to simplify the denominator (3+7)²:
(3+7)² = (10)² = 100
Now we have √7/100.
The square root of 7 cannot be simplified any further, so the simplified form with a rational denominator is:
√7/100
To simplify the expression √7/(3+7)², we can follow these steps:
Step 1: Evaluate the expression in the denominator.
(3+7)² = (10)² = 100
Step 2: Simplify the expression in the numerator.
√7 = √(7 * 1) = √(7) * √(1) = √(7)
Step 3: Rewrite the expression using the simplified numerator and denominator.
√7/(3+7)² = √7/100
So, the simplified form of √7/(3+7)² with a rational denominator is √7/100.