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.