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受欢迎的代数 >

化简 sqrt(\sqrt{2000)}

解答

化简

2000

解答

2 4 5^{3}

+1

十进制

6.68740 \dots

求解步骤

2000

2000 = 205

= 205

使用根式运算法则:

ab = a b, a \geq 0, b \geq 0

205 = 205

= 205

5 = 45

= 2045

20 = 25

= 2545

使用根式运算法则:

a = a^{\frac{1}{2}}

5 = 5^{\frac{1}{2}}

= 2 \cdot 5^{\frac{1}{2}} 45

使用根式运算法则:

n a = a^{\frac{1}{n}}

45 = 5^{\frac{1}{4}}

= 2 \cdot 5^{\frac{1}{2}} \cdot 5^{\frac{1}{4}}

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

5^{\frac{1}{2}} \cdot 5^{\frac{1}{4}} = 5^{\frac{1}{2} + \frac{1}{4}}

= 2 \cdot 5^{\frac{1}{2} + \frac{1}{4}}

\frac{1}{2} + \frac{1}{4} = \frac{3}{4}

= 2 \cdot 5^{\frac{3}{4}}

= 5^{\frac{3}{4}} \cdot 2

5^{\frac{3}{4}} = 4 5^{3}

= 4 5^{3} \cdot 2

= 2 4 5^{3}

流行的例子

solvefor u,5u-u+3u=14

so l v e f or u, 5 u - u + 3 u = 14

- 6/2

s im pl i f y 140%

solvefor x,2x=11

so l v e f or x, 2 x = 11

化简 ((9x^2-4))/((3x^2-5x+2))*((9x^4-6x^3+4x^2))/((27x^4+8x))

s im pl i f y \frac{( 9 x ^{2} - 4 )}{( 3 x ^{2} - 5 x + 2 )} \cdot \frac{( 9 x ^{4} - 6 x ^{3} + 4 x ^{2} )}{( 27 x ^{4} + 8 x )}