How do you simplify #30sqrt18-15sqrt50#?

Question

Nathan Axel · Accepted Answer

#= color(Blue)(15 sqrt2 #

#30 color(Blue)(sqrt18) -15 color(blue)(sqrt 50#

We simplify #color(blue)(sqrt18# and #color(blue)(sqrt50# by prime factorisation. (expressing a number as a product of prime factors).

#sqrt18 = sqrt ( 3 * 3 * 2 ) = sqrt ( 3^2 * 2) = color(blue)(3 sqrt2#

#sqrt50 = sqrt ( 2 * 5 * 5 ) = sqrt ( 5^2 * 2) = color(blue)(5 sqrt2#

Now the phrase is as follows:

#30 color(Blue)(sqrt18) -15 color(blue)(sqrt 50) = 30 * color(blue)(3 sqrt2) -15 * color(blue)(5 sqrt2#

#= 90sqrt2 - 75sqrt2#

Since #sqrt2# is common to both terms we take it out as a common term,

#= sqrt2 ( 90 - 75) #

#= sqrt2 (15) #

#= color(Blue)(15 sqrt2 #

Eva Adamson · Answer

undefined To simplify the expression 30√18 - 15√50, we can simplify the square roots and then combine like terms.

First, we simplify the square roots:
√18 = √(9 * 2) = 3√2
√50 = √(25 * 2) = 5√2

Now, we substitute these simplified square roots back into the expression:
30√18 - 15√50 = 30(3√2) - 15(5√2)

Next, we simplify the expression further:
30(3√2) - 15(5√2) = 90√2 - 75√2

Finally, we combine like terms:
90√2 - 75√2 = 15√2

Therefore, the simplified form of 30√18 - 15√50 is 15√2.

Julia Adams · Answer

undefined To simplify 30√18 - 15√50, first, find the prime factors of the numbers under the square roots.

√18 = √(2 × 3^2) = 3√2
√50 = √(2 × 5^2) = 5√2

Then, substitute these expressions back into the original equation:

30(3√2) - 15(5√2) = 90√2 - 75√2 = 15√2