Multiply 9 to the square root of 3 times 6 to the square root of 7. Give an exact answer

Answer 1

To multiply 9 to the square root of 3 times 6 to the square root of 7, we can write it as:

9√3 * 6√7

To multiply these expressions, we can multiply the numbers outside the square roots together and then multiply the numbers inside the square roots together. Thus, the calculation becomes:

9 * 6 * √(3 * 7)

Simplifying,

54 * √(21)

Therefore, the exact answer is 54√21.

Answer 2

Divide 2 to the square root of 65 divided by the square root of 5. Provide an exact answer

Answer 3

To divide 2 by the square root of 65 divided by the square root of 5, we can write it as:

2 / (√65 / √5)

To divide by a fraction, we can multiply by its reciprocal:

2 * (√5 / √65)

Now, let's rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator (√65 + √5).

2 * (√5 / √65) * (√65 + √5) / (√65 + √5)

Expanding the numerator:

(2√5 * √65 + 2√5 * √5) / (√65 + √5)

Simplifying:

(2√325 + 2√5) / (√65 + √5)

Therefore, the exact answer is (2√325 + 2√5) / (√65 + √5).

Answer 4

What is 2 to the square root of 65

Answer 5

2 to the square root of 65 can be written as 2^(√65).

Since the square root (√) of 65 cannot be simplified further, we will leave it as √65 in the exponent.

Thus, 2^(√65) is the exact answer.