Question

4√2 + √2 with work 8√3 - 4√3 with work 2√3 x √32 with work

Answer 1

Step-by-step explanation:

4√2 + √2 = 5√2 we add 4 and the invisible 1 in front of √2, the common root stays same

8√3 - 4√3 = 4√3 subtract 4 from 8 the common root stays same

2√3 x √32 ➡ 2√3 x 4√3 too add the expressions we first need to make the roots common then add 4 and 2

Answer 2

Answer:

1. $5\sqrt{2}$

2. $4\sqrt{3}$

3. $8\sqrt{6}$

Step-by-step explanation:

Number 1:

We can treat $\sqrt{2}$  as a variable in which we are multiplying 4 by. Let's call $\sqrt{2}$ x.

This makes our expression $4x + x$. Combining like terms, we get $5x$. This means that $4\sqrt{2} + \sqrt{2} = 5\sqrt{2}$.

Number 2:

Again, we can use the same logic as we did in number 1. Let's treat $\sqrt{3}$ as a variable y.

$8y-4y$

Subtracting a y term from a y term will equal the difference between the coefficients times y. So it's $4y$. This means that  $8\sqrt{3}-4\sqrt{3}=4\sqrt{3}$

Number 3:

When we multiply radicals, we want to put the radicals in $\sqrt{x}$ form.

$\sqrt{32}$ is already in this form.

However $2\sqrt{3}$ is not.

$2\sqrt{3}$ is the same thing as $\sqrt{3\cdot2^2} = \sqrt{3\cdot4} = \sqrt{12}$.

Now we multiply these radicals by multiply the term inside the square root sign

$\sqrt{32}\cdot\sqrt{12}=\sqrt{32\cdot12} =\sqrt{384}$

384 is divisible by 64, so:

$\sqrt{384} = \sqrt{64\cdot6} = 8\sqrt{6}$

Hope this helped!