Given the expression:
[tex] \displaystyle \large{ \sqrt{50} + \sqrt{18} - 8 \sqrt{2} }[/tex]
Since we have 2 in the square root from 8√2. We will be converting terms in √2 form so we can. evaluate.
As we know, 50 comes from 5×10 = 5×5×2
and 18 comes from 9×2 = 3×3×2.
[tex] \displaystyle \large{ \sqrt{5 \times 5 \times 2} + \sqrt{3 \times 3 \times 2} - 8 \sqrt{2} }[/tex]
In the square root, if there are two same numbers, we can pull it out as one.
Ex. √5×5 would be 5. Refer to below:
[tex] \displaystyle \large{ \sqrt{a \times a} = \sqrt{ {a}^{2} } = |a| }[/tex]
Since there are two fives and two threes in the square root, we pull these numbers out only one.
[tex] \displaystyle \large{ 5\sqrt{2} + 3 \sqrt{2} - 8 \sqrt{2} }[/tex]
Because these terms have the same square root of 2, we can evaluate 5+3-8.
[tex] \displaystyle \large{ 8 \sqrt{2} - 8 \sqrt{2} } = 0[/tex]
Of course, like term - like term = 0
Hence, the answer is 0.
