Revolutionize Your Grades with This Math Trick! | Radical Math

[@潘博宇-k4l]

E=3-2(2)^(1/2).

[@nagarajabhat4807]

√(3-2√2) could be either (√2-1) or (1-√2) as squaring both result in 3-2√2. Why is it ok to not consider the possibility of it being (1-√2)?

[@RashmiRay-c1y]

Note that (3-2√2)^1/2=√2-1, 40√2-56 = 2(√2-1). Thus, E=[61 -132(√2-1)]^1/4 = [193-132√2]^1/4. But 193-132√2 = (3-2√2)^4. Thus, E= 3-2√2.

[@Quest3669]

(193-132√2)^1/4=√(11-6√2)= 3-√2 soln.

[@Shobhamaths]

E=3-√2
√(3-2√2=√2-1
³√(-16+40√2-40)
³√x=40√2-56
x^3*=40√2-56
y^3=40√2+56
xy=4;x^3-y^3=-112
Simplify by a^3-b3 formula
x-y=-4
x^2+4x-4=0
x=2√2-2
⁴√(193-132√2)
²√(11-√18)
x=3-√2

[@gregevgeni1864]

3 - √2.
Because
3-2√2 = (√2-1)²
³√{-16+40√(3-2√2)}=³√{-16+40(√2-1)}
=³√{-56+40√2}=³√{8(-7+5√2)}=
2³√(-7+5√2)=2(√2-1) ..
⁴√{61-66³√[-16+40√(3-2√2)])=
⁴√[61-66•2(√2-1)]= ⁴√(193-132√2)=
⁴√(11-6√2)² =√(11-6√2) =√(3-√2)²= 3-√2.

[@RealQinnMalloryu4]

x^4 (61)^2 ➖(66)^2 x^3{ ➖ 16+40}:(3)^2 ➖ (2)^2 4= x^4 {3721 ➖ 36756} {x^3 *24} {9 ➖4}4={x^4 *33035} 24x^3 {5*4}={33035x^4+24x^3}={33059x^7 +20}=33079x^7 1^103^4^3^2x^3^4 1^5^5^1^2^2^1^1^x^1^2^2 2^3^2^3^1^1^^x^1^1 2^1^1^3^x 23x (x ➖ 3x+2).