How would i complete these problems?
1. (√6mn)^5
2. ^3√16x - ^3√2x^4
3.^4√x • ^3√2x
4. ^3√72x^8
5. √63a^5b • √27a^6b^4
and are these problems correct?
6. √2025xy/3√3 = 15√xy/√3
7. 3√18 + 8√50 = 49√2
8. √12 • √135 = 18√5
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6, 7 and 8 are correct.
easier to write sqrt as fractional power for these
like sqrt (x) = x^(1/2)
1.
{(6 n m )^.5}^5 = (6 m n)^(5/2)
= (6 m n)^4/2 * (6 m n)^1/2
= 36 m^2 n^2 sqrt(6 m n)
2.
(16x)^1/3) - (2x^4)^1/3 = 2 (2)^1/3 (x)^1/3 - 2^1/3 x^4/3
= 2^1/3 x^1/3( 2 - x)
3.
x^1/4 2^1/3 x^1/3
= 2^1/3 x^7/12
4.
72^1/3 x^8/3
(2^3 * 3^2)^1/3 x^8/3
2 (9)^1/3 x^8/3
5.
(3*3*7 *a^5 * b^1 *3^3 * a^6* b^4)^1/2
= (3^5 a^11 b^5)^1/2
= 9 a^5 b^2 (3 a b)^1/2
To complete these problems, we will use some basic rules of exponents and radicals. Let's go through each problem step by step:
1. To simplify (√6mn)^5, we apply the rule (a√b)^c = a^c √(b^c). So we have (√6mn)^5 = (6mn)^(5/2).
2. To simplify ^3√16x - ^3√2x^4, we can factor out common factors from each term inside the radicals. ^3√16x - ^3√2x^4 = ^3√(2x * 8) - ^3√(2x^4). Now, we can apply the rule a√(b * c) = a√b * a√c to simplify further.
3. To simplify ^4√x • ^3√2x, we use the rule a√b * a√c = a√(b * c). So we get ^4√x • ^3√2x = ^12√(x * x * 2x).
4. To simplify ^3√72x^8, we can rewrite 72 as a product of prime factors: 72 = 2^3 * 3^2. Then, we can rewrite ^3√72x^8 as ^3√(2^3 * 3^2 * x^8). We can now apply the rule (a * b)^c = a^c * b^c to simplify further.
5. To simplify √63a^5b • √27a^6b^4, we can simplify each square root separately and then multiply the resulting expressions. √63 can be simplified by breaking it down into its prime factors and taking out perfect squares. Similarly, √27 can be simplified. Then, we can multiply the simplified expressions.
Regarding the correctness of these problems, it is difficult for me to verify it without the values of the variables (m, n, x, y, a, b). Please provide the numerical values for these variables if you would like me to verify the solutions.
For problem 6, √2025xy/3√3 = 15√xy/√3, the simplification is incorrect. To simplify it correctly, we need to rationalize the denominator by multiplying it by its conjugate, which is √3. So the correct simplification is (15√xy)/√3 * √3/√3 = (15√3xy)/3 = 5√3xy.
Similarly, for problem 7, 3√18 + 8√50 = 49√2, the simplification is incorrect. To simplify it correctly, we need to simplify the radicals and then add the terms.
For problem 8, √12 • √135 = 18√5, the simplification is correct since we can multiply the numbers under the square roots and then simplify further.
Note: Please make sure to use parentheses and provide more specific information if there are any uncertainties or variations in the problems.