Reduce the root sign of quadratic radical (- 5) 2 X3 1. - 5 radical sign 3 2.5 radical sign 3

Reduce the root sign of quadratic radical (- 5) 2 X3 1. - 5 radical sign 3 2.5 radical sign 3

√（- 5）² × 3
=1 - 5 ×√ 3
= 5√3

Reduction of root sign {[(radical 8) - 1] 2 + [radical 8) - 1] 2}

Root sign [(root 8) - 1] 2 + [root 8) - 1] 2
=Radical [8 + 1-2 (radical 8)] + [8 + 1 + 2 (radical 8)]
=Radical (9 + 9)
=Radical (18)
=3 pieces (2)

First, simplify and then evaluate (1 + x) fractions (x 2 + 2x) / {X - (x + 1) fractions 2} - 1, where x = root 2 + 1 / 1

x=1/(√2+1)=√2-1
The original formula = x (x + 2) / (x + 1) / (x 2 + X-2) / (x + 1) - 1
=x(x+2)/(x+1)*(x+1)/(x+2)(x-1)-1
=x/(x-1)-1
=(x-x+1)/(x-1)
=1/(x-1)
=1/(√2-1-1)
=(√2+2)/(2-4)
=-(√2+2)/2

First simplify and then evaluate x 2-1 ^ (2x-1 of 1-x), where x = radical 2 X? - 1 ^ (2x-1 of 1-x) is x? - 1 ^ (2x-1 of 1-x)

=(x+1)(x-1)/x÷ (x-2x+1)/x
=(x+1)(x-1)/x×[-x/(x-1)=
=x+1
When x = √ 2
Original formula = √ 2 + 1

(1 + 2X-4 / x? - X-2) △ x + 3 / x? - 1, simplify and then evaluate x = radical 3

1+(2x-4)/(x^2-a-2)]/[(x+3)/(x^2-1)]
={1+2(x-2)/[(x-2)(x+1)]}(x^2-1)/(x+3)
=[1+2/(x+1)](x+1)(x-1)/(x+3)
=[x+1+2](x-1)/(x+3)
=x-1
X = √ 3 (root 3)
The original formula = √ 3-1

First simplify, then evaluate: (1) (x + 1 / x? - x-x / x? - 2x + 1) △ 1 / x, x = radical 2 + 1 (2) (1 + x-3 / x + 3) △ 2x / x? - 9 x = radical 3 + 3 (3) 4-x / X-2 ^ (x + 2-12 / X-2) x = radical 3-4 (4) x-3 / 2X-4 ^ (5 / x-2-x-2) x = radical 3-2

First simplify, then evaluate: (1) (x + 1 / x? - x-x / x? - 2x + 1) ÷ 1 / x, x = radical 2 + 1! = ((x + 1) / X (x-1) - X / (x-1) 2) × x = (x + 1) / (x-1) - X / (x-1) 2 = (x? - 1-x?) / (x-1) Ω) / (x-1) x2 = - 1 / (√ 2 + 1-1) mm2 = - 1 / 2; (2) (1

X ＞ 3, simplify the root number x 2 - 6x + 9 + the root sign x 2 + 2x + 1

Root x? 6x + 9 + root x? 2 + 2x + 1
=Root (x-3) 2 + root (x + 1) 2
=x-3+x+1
=2x-2

When x > 3, the (3-x) radical 2x / 9-6x + X? Is reduced

（3-x）√2x/9-6x+x²
=(3-x)√2x/(3-x)²
=(3-x)/(x-3)√2x
=-√2x

Simplification: - 2 ＜ x ＜ 2, radical x  2 + 2x + 1 + root sign system 2 - 6x + 9

-1

Simplify 1 / 6x radical 18x-x? Radical 1 / 2x

1 / 6x root 18x-x? Root 1 / 2x
=1/2x√2x-1/2x√2x
=0