Find the square root of 170 - 20\(\sqrt{30}\)
2 \(\sqrt{10}\) - 5\(\sqrt{3}\)
2 \(\sqrt{5}\) - 5\(\sqrt{6}\)
5 \(\sqrt{10}\) - 2\(\sqrt{3}\)
3 \(\sqrt{5}\) - 8\(\sqrt{6}\)
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et's say
√(170 - 20√30) = √a - √b
square both sides.
170 - 20√30 = (√a - √b)²
170 - 20√30 = a - 2√ab + b
170 - 20√30 = a + b - 2√ab
comparing coefficient
a + b = 170
a = 170 - b ----- (1)
-2√ab = -20√30
√ab = 10√30
square both sides.
ab = 100(30)
ab = 3000------(2)
sub (1) into (2)
b(170 - b) = 3000
170b - b² = 3000
b² - 170b + 3000 = 0
b² - 150b - 20b + 3000 = 0
b(b - 150) - 20(b - 150) = 0
b = 20 or 150
sub b in (1)
a = 170 - b
a = 150 or 20
Re : √(170 - 20√30) = √a - √b
= √150 - √20
=√25x6 - √5x4
=5√6 - 2√5
Note use this formula specifically for this equation, it's more faster, if you can cram it better for you but use it specifically for this equation;because it's a perfect square
or you can use plug and play
For option B
it 2 sqr root 5 and 5 sqr root 6
is 2×2×5,5×5×6. which is 150 plus
or you can use plug and play
For option B
it 2 sqr root 5 and 5 sqr root 6
is 2×2×5,5×5×6. which is 150 plus 20 which is 170
