Multiply nine square root of 3 × 6 square root of seven give an exact answer
To multiply the expressions "nine square root of 3" and "6 square root of seven," you can simplify each square root separately and then multiply the resulting numbers together.
First, simplify the square root of 3. Since there are no perfect square factors of 3, the square root of 3 remains as it is: √3.
Next, simplify the square root of seven. There are no perfect square factors of 7 either, so the square root of seven remains: √7.
Now, multiply the numbers: 9 * 6 = 54.
Finally, combine the square roots with the multiplied number: 54√3√7.
However, we can simplify this further. The product of two square roots (√3 * √7) is equal to the square root of their product (√(3 * 7)).
So, 54√3√7 becomes 54√(3 * 7) = 54√21.
Therefore, the exact answer is 54√21.
To multiply expressions that involve square roots, you can follow these steps:
Step 1: Multiply the coefficients (numbers) together.
9 × 6 = 54
Step 2: Multiply the square roots together.
√3 × √7 = √(3 × 7) = √21
Step 3: Combine the results from Step 1 and Step 2.
54√21
Therefore, the exact answer to the multiplication of 9√3 × 6√7 is 54√21.
To multiply two square roots, we can multiply the numbers outside the square roots and simplify any square roots that we can.
First, let's simplify each square root individually:
√3 can't be simplified any further because 3 is a prime number.
√7 can't be simplified any further because 7 is a prime number.
Now, let's multiply the numbers outside the square roots:
9 × 6 = 54.
Finally, we write the final answer by multiplying the square roots together and simplifying if possible:
√3 × √7 = √(3 × 7) = √21.
Putting it all together, the exact answer is:
9 √3 × 6 √7 = 54 √21.