Simplify 7√99.(1 point)
To simplify the expression 7√99, we can rewrite 99 as the product of a perfect square and another number. The largest perfect square that divides evenly into 99 is 9, so we can rewrite 99 as 9 * 11.
Now we can simplify the expression further:
7√99 = 7√(9 * 11)
Since the square root of 9 is 3, we can simplify the expression again:
7√99 = 7 * 3√11
Therefore, the simplified expression is 21√11.
To simplify 7√99, we can break down 99 into its prime factors. The prime factorization of 99 is 3 × 3 × 11.
Therefore, 7√99 can be written as 7√(3 × 3 × 11).
Simplifying further, we can take the square root of each individual factor.
The square root of 3 × 3 is 3, and the square root of 11 is √11.
So, 7√99 simplifies to 7 × 3 × √11 = 21√11.
To simplify the expression 7√99, we can break down 99 into its prime factors and simplify the square roots if possible.
Step 1: Find the prime factors of 99.
99 = 3 × 3 × 11
Step 2: Simplify the square root of each prime factor.
√3 × √3 × √11 = 3√11
Step 3: Substitute the simplified square roots back into the original expression.
7√99 = 7(3√11) = 21√11
Therefore, the simplified form of 7√99 is 21√11.