Multiply 9 to the square root of 3 times 6 to the square root of 7. Give an exact answer
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.
To multiply 9 by the square root of 3 times 6 by the square root of 7, first, we can simplify the square roots.
The square root of 3 cannot be simplified because it is not a perfect square.
The square root of 7 also cannot be simplified because it is not a perfect square.
Next, we can multiply the numbers:
9 * √3 * 6 * √7
To multiply the numbers, we can combine the coefficients (numbers outside the square roots) and the square roots:
9 * 6 * √(3 * 7)
Multiplying the coefficients, we get:
54 * √(21)
Therefore, the exact answer is 54 times the square root of 21.
To solve this problem, we need to calculate the product of 9 times the square root of 3, and then multiply that by 6 times the square root of 7. Let's break it down step by step.
Step 1: Calculate 9 times the square root of 3.
- Recall that the square root (√) of a number can be calculated using the exponent of 0.5. In this case, the square root of 3 is √3.
- Multiply this value by 9: 9 * √3.
Step 2: Calculate 6 times the square root of 7.
- Again, find the square root of 7: √7.
- Multiply this value by 6: 6 * √7.
Step 3: Multiply the two results from Step 1 and Step 2.
- Multiply 9 * √3 and 6 * √7 together to obtain the final result.
So the exact multiplication of 9 times the square root of 3 times 6 times the square root of 7 is:
(9 * √3) * (6 * √7).
To simplify further, we can multiply the coefficients (9 * 6 = 54), and multiply the square root terms (√3 * √7 = √(3 * 7) = √21).
Therefore, the exact answer is 54√21.
Divide 2 to the square root of 65 divided by the square root of 5. Provide an exact answer
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).
What is 2 to the square root of 65
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.