simplify the expressions.
1. sqrt(40/169)
2. sqrt(18/13)
3. sqrt(45/32)
first factor numerators and denominatios
40 = 2*2*2*5
so
sqrt 40 = 2 sqrt 10
169 = 13 * 13
so
sqrt 169 = 13
so we have
(2/13) sqrt 10
what about the other ones?
i don't understand these at all.
There is no point in my just doing them all for you. Please study the one I did.
for each of them factor and look for squares
like 18 = 2*9 = 2 * 3 * 3
therefore sqrt 18 = 3 sqrt 2
there is nothing you could do with sqrt 13 or sqrt 3 or sqrt 7 or sqrt 11 for example because those are already prime numbers and do not contain smaller factors except 1. However where there are factors, find them and see if any are repeated.
okay thank you. :)
To simplify the given expressions, we can simplify the square roots using the following steps:
1. sqrt(40/169):
To simplify sqrt(40/169), we can simplify both the numerator and the denominator under the square root separately. The perfect square factors of 40 are 4 and 10 (since 4 * 10 = 40), and the perfect square factor of 169 is 13 (since 13 * 13 = 169). Simplifying the expression, we get:
sqrt(40/169) = sqrt((4 * 10)/(13 * 13))
= sqrt(4/13) * sqrt(10/13)
= (2/13) * sqrt(10)
2. sqrt(18/13):
Similarly, for sqrt(18/13), we can simplify the numerator and denominator separately. The perfect square factors of 18 are 9 and 2 (since 9 * 2 = 18), and the perfect square factor of 13 is 13 itself. Simplifying the expression, we get:
sqrt(18/13) = sqrt((9 * 2)/13)
= sqrt(9/13) * sqrt(2/13)
= (3/13) * sqrt(2)
3. sqrt(45/32):
For sqrt(45/32), we simplify the numerator and denominator using perfect square factors. The perfect square factors of 45 are 9 and 5 (since 9 * 5 = 45), and the perfect square factors of 32 are 16 and 2 (since 16 * 2 = 32). Simplifying the expression, we have:
sqrt(45/32) = sqrt((9 * 5)/(16 * 2))
= sqrt(9/16) * sqrt(5/2)
= (3/4) * sqrt(5/2)
Therefore, the simplified expressions are:
1. sqrt(40/169) = (2/13) * sqrt(10)
2. sqrt(18/13) = (3/13) * sqrt(2)
3. sqrt(45/32) = (3/4) * sqrt(5/2)