How do you calculate FOIL in working with Square roots?

Answer 1

Let's take an example.

(√(5) + 2) (√(3) + 1)

First, do the FOIL.

√(5)√(3) + √(5) + 2√(3) + 2

We can multiply square roots together by multiplying their insides.

√(15) + √(5) + 2√(3) + 2

Example #2 (and one of the more common ones):

(√(2) + 3)^2

First, this is equivalent to

(√(2) + 3)(√(2) + 3)

FOILing this out,

[√(2)]^2 + 3√(2) + 3√(2) + 3(3)

But, the square of a square root is just itself; squaring the radical will eliminate the radical.

2 + 6√(2) + 9

Now, we can simplify even further.

11 + 6√(2)

Answer 2

FOIL = First Inside Outside Last

raising a number to the 1/2 power the same as taking the square root of the number. For example, 36^(1/2) = 6.

Remember that, when solving an equation, you can do whatever you like to it, as long as you do the same thing to both sides. On the left-hand side

To show you why the "1/2 power" of a number means the same as "square
root" of the number, I need to give a little background first. Let's
try this...

The square root of 9 is 3 because 3^2 = 3 * 3 = 9.

The square root of 64 is 8 because 8^2 = 8 * 8 = 64.

In summary, the square root of some number N is a value that when
multiplied by itself (or squared) produces the given number N. Or in
other words, r will be the square root of N if r^2 or r * r = N.

Are you familiar with the basic laws of exponents? Let's apply some
of them to this question. We'll start with:

x^a * x^b = x^(a + b)

This law says that when you multiply like bases, you keep the base and
add the exponents, as shown here:

x^2 * x^3 = (x*x)*(x*x*x) = x*x*x*x*x = x^5, which is x^(2 + 3)

Let's try using that law with the 1/2 power:

x^(1/2) * x^(1/2) = x^(1/2 + 1/2) = x^1 = x

But look at what just happened! We multiplied x^(1/2) by itself (or
squared it) and we got x. According to our earlier summary/definition
of the square root, that means that x^(1/2) must be the square root of
x. Can you see that?

Here's one more way to look at it using exponent laws. There is a law
that says that a power raised to a power is the product of the powers.
In other words:

(x^2)^3 = x^(2*3) or x^6

This is actually an extension of the exponent addition rule we already
looked at, since

(x^2)^3 = x^2 * x^2 * x^2 = x^(2 + 2 + 2) = x^6

Let's suppose for a moment that we don't know how to write a square
root as an exponent, and we'll try to figure out what would work. We
know that when we square the square root of x we will get x, as we
defined above. So if we let n be this unknown exponent that
represents the square root of x, we know that

(x^n)^2 = x

Applying our "power to a power" rule, we can rewrite that equation as

x^(2n) = x^1

Since the bases are the same on each side of the equation (x), and the
two quantities are equal, the exponents must also be the same:

2n = 1
n = 1/2

Ahah! The mystery exponent n that represents the square root turns
out to be 1/2.

You can see why it works:

[x^(1/2)]^2 = x^[(1/2) * 2] = x^1 = x

Going back to your example:

[36^(1/2)] * [36^(1/2)] = [36^(1/2)]^2 = 36^[(1/2) * 2] = 36^1 = 36

Since multiplying 36^(1/2) by itself (or squaring it) gave 36,
36^(1/2) must in fact be the square root of 36.

Answer 3

better ask ur teacher

Answer 4

please explain in more detail cuz i dun knwo what your talkin bout