What is the square root of 6 times the square root of 9 if there is no perfect square of 6
the square root of 9 is 3, so the 6 x 3 = 18, so the square root of 18. This can be written as 3square root 2.
"Dr. Cuddy" is incorrect
√9 x √6
= 3√6
Oh yes, sorry my mistake. 3�ã6 is the correct answer.
To find the value of the square root of 6 times the square root of 9, let's break it down step by step.
Step 1: Simplify the square roots individually.
The square root of 6 cannot be simplified further since there is no perfect square that divides evenly into 6. The square root of 9 is 3 because 3 times 3 equals 9, making 9 a perfect square.
Step 2: Multiply the simplified square roots.
The square root of 6 multiplied by the square root of 9 is equal to the square root of 6 times 3, which can be written as √6 * √9 or √(6 * 9).
Step 3: Calculate the multiplication inside the square root.
The product of 6 and 9 is 54. Therefore, √(6 * 9) is equivalent to √54.
Step 4: Simplify the square root expression of 54.
To simplify √54, we need to find the largest perfect square that divides evenly into 54. The largest perfect square that divides evenly into 54 is 9, which is 3^2.
Step 5: Rewrite the square root of 54.
√54 can be rewritten as √(9 * 6).
Step 6: Simplify the square root expression further.
Since 9 is a perfect square, we can take the square root of it without any remaining factors. The square root of 9 is 3.
Step 7: Complete the calculation.
√(9 * 6) can be written as 3 * √6.
Therefore, the square root of 6 times the square root of 9 is 3√6.