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:
1. [tex]5\sqrt{2}[/tex]
2. [tex]4\sqrt{3}[/tex]
3. [tex]8\sqrt{6}[/tex]
Step-by-step explanation:
Number 1:
We can treat [tex]\sqrt{2}[/tex] as a variable in which we are multiplying 4 by. Let's call [tex]\sqrt{2}[/tex] x.
This makes our expression [tex]4x + x[/tex]. Combining like terms, we get [tex]5x[/tex]. This means that [tex]4\sqrt{2} + \sqrt{2} = 5\sqrt{2}[/tex].
Number 2:
Again, we can use the same logic as we did in number 1. Let's treat [tex]\sqrt{3}[/tex] as a variable y.
[tex]8y-4y[/tex]
Subtracting a y term from a y term will equal the difference between the coefficients times y. So it's [tex]4y[/tex]. This means that [tex]8\sqrt{3}-4\sqrt{3}=4\sqrt{3}[/tex]
Number 3:
When we multiply radicals, we want to put the radicals in [tex]\sqrt{x}[/tex] form.
[tex]\sqrt{32}[/tex] is already in this form.
However [tex]2\sqrt{3}[/tex] is not.
[tex]2\sqrt{3}[/tex] is the same thing as [tex]\sqrt{3\cdot2^2} = \sqrt{3\cdot4} = \sqrt{12}[/tex].
Now we multiply these radicals by multiply the term inside the square root sign
[tex]\sqrt{32}\cdot\sqrt{12}=\sqrt{32\cdot12} =\sqrt{384}[/tex]
384 is divisible by 64, so:
[tex]\sqrt{384} = \sqrt{64\cdot6} = 8\sqrt{6}[/tex]
Hope this helped!
