alright i have a few questions if its ok..?
Simplify:
1. -2√(96a^5)
2.√(x+6)^7
3.√18a^5b * √12ab^3
4.√7/8
5. 2√10/6√50
6.1/3√27+27√1/3
7.Solve: √(2x-7) + 3=8
Thanks so much! really appreciate it!
I'll do number 7. Bringing the 3 over as a minus 3, we have �ã(2x-7)=5, square both sides to get rid of the square root sign and we have 2x-7=25, 2x=32, x=16
Of course! I'd be happy to help you with your questions. Let's go through each question step by step:
1. Simplify: -2√(96a^5)
To simplify this expression, we can begin by breaking down the radicand (the number inside the square root symbol) into its factors. In this case, the radicand is 96a^5. We can write it as follows:
-2√(2^5 * 3 * a^5)
Next, we can take out any perfect square factors from under the square root. In this case, 2^5 can be simplified as 2^2 * 2^2 * 2, which becomes 4 * 4 * 2 = 32. The square root of 32 can be further simplified as 4√2.
Therefore, the simplified expression is: -64a√2.
2. Simplify: √(x+6)^7
To simplify this expression, we can expand the exponent to its entire expression within the square root. In this case, we have:
√(x+6) * √(x+6) * √(x+6) * √(x+6) * √(x+6) * √(x+6) * √(x+6)
When multiplying square roots, we can combine like terms under the root symbol. So we can rewrite it as follows:
(x+6)^3 * √(x+6)
Therefore, the simplified expression is: (x+6)^3 * √(x+6).
3. Simplify: √18a^5b * √12ab^3
To simplify this expression, we can multiply the numbers and variables outside of the square roots together. In this case, we have:
√(18a^5b) * √(12ab^3)
Multiplying these together, we get:
√(18 * 12 * a^5 * a * b * b^3)
Simplifying further:
√(216 * a^6 * b^4)
Breaking down 216 into its factors:
√(2^3 * 3^3 * a^6 * b^4)
Taking out any perfect square factors:
6ab^2 * √(2a^2)
Therefore, the simplified expression is: 6ab^2√(2a^2).
4. Simplify: √7/8
To simplify this expression, we can write it as a single fraction. The square root can be placed over a square root. So we have:
√(7) / √(8)
To simplify the denominator, we can find perfect squares. The square root of 8 can be simplified as √(4 * 2) = 2√2.
Therefore, the simplified expression is: √7 / 2√2.
But to get rid of the square root in the denominator, we can multiply the numerator and denominator by √2:
(√7 / 2√2) * (√2 / √2)
Multiplying the numerators and the denominators:
√14 / 2√(2 * 2)
Simplifying further:
√14 / 4
Therefore, the final simplified expression is: √14 / 4.
5. Simplify: 2√10 / 6√50
To simplify this expression, we can rationalize the denominator. Multiply both the numerator and denominator by the conjugate of the denominator. In this case, the conjugate of √50 is √50.
(2√10 / 6√50) * (√50 / √50)
Multiplying the numerators and denominators:
2√(10 * 50) / (6√50 * √50)
Simplifying further:
2√(500) / 6 * 50
Breaking down 500 into its factors:
2√(2^2 * 5^2 * 5)
Simplifying further:
2 * 5 * √2 / 6 * 5
Canceling out common factors:
√2 / 3
Therefore, the simplified expression is: √2 / 3.
6. Simplify: 1/3√27 + 27√1/3
To simplify this expression, we can simplify each term separately and then combine them.
For 1/3√27, we can simplify the square root of 27, which is 3√(3). So we have:
1/3 * 3√(3)
Simplifying further:
√(3) / √(3) = 1
For 27√1/3, we can simplify the square root of 1/3. So we have:
27 * 1/√(3)
Multiplying the numerators and denominators:
27 / √(3)
To rationalize the denominator, we can multiply both the numerator and denominator by √3:
(27 / √(3)) * (√(3) / √(3))
Multiplying the numerators and denominators:
27√3 / √(3 * 3)
Simplifying further:
27√3 / 3
Canceling out the common factor:
9√3
Finally, we can add the two simplified terms together: 1 + 9√3.
Therefore, the simplified expression is: 1 + 9√3.
7. Solve: √(2x-7) + 3 = 8
To solve this equation, we can isolate the square root term and then square both sides to get rid of the square root.
Subtracting 3 from both sides of the equation, we have:
√(2x-7) = 8 - 3
√(2x-7) = 5
Next, we'll square both sides of the equation to eliminate the square root:
(√(2x-7))^2 = 5^2
2x-7 = 25
Adding 7 to both sides of the equation, we get:
2x = 32
Finally, divide both sides by 2:
x = 16
Therefore, the solution to the equation √(2x-7) + 3 = 8 is x = 16.
I hope this helps! Let me know if you have any further questions.