what is the answer to \/12 + 3\/72 ??? *\/ means sqaure root. & what is the formula for doing these questions

Answer 1

One way is to find the factors of the number under the root. Then, like any other equation, you can gather like terms.

√12 = √(4*3) = √4 * √3 = 2*√3
3*√72 = 3*√(36*2) = 3* √36 * √2 = 3*6*√2

Using the above:
√12 + 3*√72 =
2*√3 + 18*√2

And you cannot simplify further unless you use approximations.

√3 = 1.7320508...
√2 = 1.4142135...

Answer 2

sqrt(12) + 3sqrt(72)

What you're going to do is a technique to simplify radicals. What you want to do is obtain the prime factorization of each number. Note that
12 = 4 x 3 = 2 x 2 x 3
72 = 8 x 9 = 2 x 2 x 2 x 3 x 3

Replacing 12 with (2)(2)(3) and 72 with (2)(2)(2)(3)(3), we have

sqrt [(2)(2)(3)] + 3sqrt[(2)(2)(2)(3)(3)]

Now, for EVERY two identical numbers inside the square root, you're going to cancel them out, and pull them outside the square root. When you pull them in front of the square root, they become a single. For sqrt(2*2*3), we see two 2s; we pull them out of the square root as a single, obtaining 2sqrt(3).
Repeat this process for the second radical; there are two 2s and two 3s, so they get pulled out of the square root as (2)(3). What we have is the following:

2sqrt(3) + 3(2)(2)sqrt(2)

Simplifying this, we have

2sqrt(3) + 12sqrt(2)

Was that confusing for you? Here's an alternative method, slightly advanced.

sqrt(12) = sqrt(4 * 3)
sqrt(72) = sqrt(36 * 2)

4 and 36 are both square numbers. By the square root property sqrt(a * b) = sqrt(a)sqrt(b),

sqrt(12) = sqrt(4)sqrt(3) = 2sqrt(3)
sqrt(72) = sqrt(36)sqrt(2) = 6sqrt(2)

{The square root of 4 is 2, the square root of 36 is 6.}

If you're able to successfully get a perfect square inside a square root, it gets pulled out as a single square root. It takes practice to get used to this, but I suggest you do a lot of questions so you get good at recognizing this. Math is all about recognizing patterns.

Answer 3

V12 + 3V 72 = V (3*4) + 3 V (9*8) = V3 V4 + 3 V9 V 8

V4 = 2 and V9 = 3
V8 = V(4*2) = V4 * V2 = 2V2

So, V12 + 3V72 = 2V3 + (3*3) (2V2) = 2V3 + 18V2

This is a way to work with this expression. Another one could be this one:

V12 + 3V72 = V12 + 3V(6*12) = V12 + 3 V6 V12

And then you can factorize:

V12 (1 + 3V6) = V4 V3 (1+ 3V3V2) = 3V2 [1+ V(3^3)V2]

There are many things that you can do here. I dont know what exactly you are supposed to do, but I hope that this helps you.

Ana

Answer 4

The trick is factoring what's under the square root sign. Rewrite sqrt(12) + 3*sqrt(72) as sqrt(4*3) + 3*sqrt(36*2), because what you want to do is pull out square factors, and write the square root of a product as the product of square roots, like so: 3*sqrt(4)*sqrt(3) + 3*sqrt(36)*sqrt(2), and then evaluate the square roots, to get 3*2*sqrt(3) + 3*6*sqrt(2) = 6*sqrt(3) + 18*sqrt(2).

Answer 5

V12 + 3V72
= V3*2^2 + 3V2*6^2
= 2V3 + 3*6V2
= 2V3 + 18V2

buddy theres no formula, you have to learn the sq rt properties for doing these.

nexus

Answer 6

sqrt(12) + 3sqrt(72)
sqrt(4 * 3) + 3sqrt(36 * 2)
2sqrt(3) + 18sqrt(2)

Since the 2 values do now have the same sqrt value, you can't simplify.