The slash (/) line represents that the number is a fraction.
divide:
sqrt45 / sqrt81 =
simplify:
7sqrt3 / sqrt5 =
Multiply:
sqrt7/sqrt8 X sqrt24/sqrt49 =
Thanks for the advice regarding how to show square root symbol correctly. Also thank for taking the time to help with these problems. I have a total of 12 to do and I do not know to get started on these 3 at all. Thank you.
divide:
sqrt45 / sqrt81 = 2.236067977
simplify:
7sqrt3 / sqrt5 = 8.108045297
Multiply:
sqrt7/sqrt8 X sqrt24/sqrt49 = 2.140695143
that's wrong
see
http://www.jiskha.com/display.cgi?id=1319940791
To solve these problems involving square roots, we can use the basic properties of square roots. Here's how to solve each problem step by step:
1. Divide: sqrt(45) / sqrt(81)
To divide square roots, use the property that the square root of a product is equal to the product of the square roots. So, sqrt(a) / sqrt(b) = sqrt(a/b).
sqrt(45) / sqrt(81) = sqrt(45 / 81)
Now simplify the fraction 45/81 by dividing both numerator and denominator by their greatest common divisor, which is 9.
45/81 = 5/9
Therefore, sqrt(45) / sqrt(81) = sqrt(5/9) = sqrt(5)/sqrt(9).
However, we know that sqrt(9) = 3, so the final answer is:
sqrt(5) / 3
2. Simplify: 7sqrt(3) / sqrt(5)
To simplify this expression, we use the property that the square root of a product is equal to the product of the square roots. So, sqrt(a) / sqrt(b) = sqrt(a/b).
7sqrt(3) / sqrt(5) = 7sqrt(3 / 5)
Since there are no perfect square factors in the numerator or denominator, we cannot simplify it any further.
Therefore, the simplified expression is:
7sqrt(3) / sqrt(5)
3. Multiply: sqrt(7) / sqrt(8) * sqrt(24) / sqrt(49)
To multiply square roots, use the property that the square root of a product is equal to the product of the square roots. So, sqrt(a) * sqrt(b) = sqrt(a*b).
sqrt(7) / sqrt(8) * sqrt(24) / sqrt(49) = sqrt(7*24) / sqrt(8*49) = sqrt(168) / sqrt(392)
Now, let's simplify each square root individually:
sqrt(168) = sqrt(4*42) = sqrt(4) * sqrt(42) = 2sqrt(42)
sqrt(392) = sqrt(4*98) = sqrt(4) * sqrt(98) = 2sqrt(98)
Therefore, the expression becomes:
(2sqrt(42)) / (2sqrt(98))
Next, notice that both the numerator and denominator have a common factor of 2. Cancel out this common factor:
(2sqrt(42)) / (2sqrt(98)) = sqrt(42) / sqrt(98)
Lastly, we can simplify the square roots further:
sqrt(42) = sqrt(7*6) = sqrt(7) * sqrt(6)
sqrt(98) = sqrt(7*14) = sqrt(7) * sqrt(14)
Therefore, the expression becomes:
(sqrt(7) * sqrt(6)) / (sqrt(7) * sqrt(14))
The sqrt(7) term cancels out:
(sqrt(7) * sqrt(6)) / (sqrt(7) * sqrt(14)) = sqrt(6) / sqrt(14)
Hence, the final answer is:
sqrt(6) / sqrt(14)
Remember to simplify the fraction if possible, but in this case, there are no common factors between the numerator and denominator, so we cannot simplify it further.