Simplify 7√99 .
We can simplify 7√99 by finding the largest perfect square that divides evenly into 99. The largest perfect square that divides evenly into 99 is 9, which is equal to 3^2.
So we can rewrite 7√99 as 7√(9*11) .
Taking the square root of 9, we get 3.
So 7√(9*11) = 7 * 3√11 .
Therefore, the simplified form of 7√99 is 21√11 . Answer: \boxed{21\sqrt{11}}.
To simplify 7√99, we can break it down step-by-step.
Step 1: Determine the prime factors of 99.
99 can be broken down as follows:
99 = 3 * 3 * 11
Step 2: Rewrite the square root expression.
√99 = √(3 * 3 * 11)
Step 3: Pull out the perfect squares from under the square root.
√(3 * 3 * 11) = √(3 * 3) * √11 = 3√11
Step 4: Multiply the simplified expression by 7.
7√99 = 7 * 3√11 = 21√11
So, the simplified form of 7√99 is 21√11.
To simplify the expression 7√99, we need to find the factor of 99 that is a perfect square.
Step 1: Find the prime factorization of 99:
99 = 3 × 3 × 11
Step 2: Identify the perfect square factors:
We see that 9 (3 × 3) is a perfect square factor of 99.
Step 3: Rewrite the expression using the square root of the perfect square factor:
7√99 = 7√(9 × 11)
Step 4: Simplify the expression:
Using the property of square roots that states √(ab) = √a × √b, we can rewrite the expression as follows:
7√(9 × 11) = 7√9 × √11
Step 5: Evaluate the square root of the perfect square:
The square root of 9 is 3, so we have:
7√9 × √11 = 7 × 3 × √11 = 21√11
Therefore, the simplified form of 7√99 is 21√11.