Verified answer

√(9x^2 + 36x + 36) = 3√(x^2 + 4x + 4) = 3√(x + 2)^2 = 3|x + 2|

When taking a square root, you must take care that the stuff under the radical sign be non-negative, and that the square root also be non-negative.

√(a^2) = |a|

The absolute value here is essential; without it, you will get failure of the equality, e.g., when a is negative.

Beware; of the 9 answers up here so far, only Ed I and I have this in our answers.

√(9x^2 + 36x + 36) = 3√(x^2 + 4x + 4) = 3√(x + 2)^2 = 3|x + 2|

9x^2 + 36x + 36 = 9(x^2 + 4x + 4) = 9(x + 2)(x + 2)

so square root of 9(x+2)(x+ 2) = 3(x +2)

You have to factor the inside expression (I'm going to use | for root)

First find the Greatest common factor which is 9

You take that out so the new problem is

|9(x2+4x+4)

since 9 is a coefficient and there is no other term you can take it's root out 3|(x2+4x+4)

then you find the factors of the third term 4

2-2, 4-1

You find out which of those added together will get you the middle term 4

You the make two terms (x+2)(x+2)

since there are two of x+2 the term x2+4x+4 is a perfect square with it's root as x+2 so you can take it out of the root

You are left with 3(x+2) as your answer

Hope I helped :)

Common factor Of 3, so Put 3 outside of the root and begin factorising

3 sqrt x^2 +4x +4

x^2+4x+4 = (x+2)^2

We need to get rid of the square root, so we square the brackets.

3 sqrt ((x+2)^2)

3(x+2)

3x+6

√(9x² + 36x + 36)

√(9(x² + 4x + 4))

3√(x² + 4x + 4)

3√((x + 2)(x + 2))

3√(x + 2)²

3(x + 2)

3x + 6

i'm unlikely to respond to all of them, yet i visit instruct you the thank you to do the harder ones. :) for #2 you have (7b2 – 5b + 3) – (b2 + 8b – 6). as a manner to unravel this you ought to distribute the detrimental to the 2nd term. you get 7b^2 - 5b +3 - b^2 - 8b + 6. then you definately combine like words (7b^2 with -b^2, -5b with -8b and +3 with +6) you're left with 6b^2 - 13b +9 (answer b) to do #a million, you easy distribute the useful to the 2nd term (which adjustments no longer something), and resolve interior a similar way. for #4, you ought to distribute the numbers outdoors of the parenthesis to get the respond. 6k(4k + ok^2) + 9k(2k - 6k^2) you multiply 6k by skill of 4k, and 6k by skill of ok^2 to get 24k^2 + 6k^3, then distribute the 9k to the 2nd term. you get 24k^2 + 6k^3 + 18k^2 - 54k^3. combine like words to get -42k^2 - 48k^3 (answer c) for #7 you ought to apply the FOIL technique of distribution. (g^2 + 4)(4g^2 + 8g - 9) you multiply g^2 to 4g^2, +8g and -9 to get 4g^4 + 8g^3 - 9g^2 then you multiply +4 to 4g^2, +8g and -9 to get 16g^2 + 32g - 36. you're left with 4g^4 + 8g^3 - 9g^2 + 16g^2 + 32g - 36 you (wager what) combine like words. 4g^4 + 8g^3 + 7g^2 + 32g - 36 (answer c) finally, for #10 you ought to element out the GCF (astounding elementary element - the smallest variety that is going into each and every variety) considering which you have 18v^4 + 27v^3 + 36v^2, GCF may well be 9v^2 by way of fact it divides flippantly into each and every variety interior the expression. you're left with 9v^2(2v^2 + 3v +4) (answer a). You resolve the different factoring questions in an identical way. :) wish i ought to help!

sqrt (9x^2 +36x + 36)

= sqrt (3x + 6)^2

=3x +6

= 3(x + 2)

sqrt(9x^2 + 36x + 36)

sqrt(9)sqrt(x^2 + 4x + 4)

3sqrt(x2 + 4x + 4)

3sqrt((x + 2)^2)

3(x + 2)

9x^2 + 36x + 36 = (3x+6)(3x+6) = (3x+6)^2

√(3x+6)^2 = 3x+6

Hope this helps!