What is 10^8*(sqrt(371))/(20sqrt(5)) ?

The solution to 10^8*(sqrt(371))/(20sqrt(5)) is 1000000sqrt(1855)

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simplify 10^8*(sqrt(371))/(20sqrt(5))

simplify

1 0^{8} \cdot \frac{371}{20 5}

10000001855

Decimal Notation

43069710.93471 \dots

Solution steps

1 0^{8} \cdot \frac{371}{20 5}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{371 \cdot 1 0 ^{8}}{20 5}

Factor

1 0^{8} : 2^{8} \cdot 5^{8}

Factor

20 : 2^{2} \cdot 5

= \frac{2 ^{8} \cdot 5 ^{8} 371}{2 ^{2} \cdot 5 5}

Cancel

\frac{371 \cdot 2 ^{8} \cdot 5 ^{8}}{2 ^{2} \cdot 5 5} : \frac{5 ^{7} \cdot 2 ^{6} 371}{5}

= \frac{5 ^{7} \cdot 2 ^{6} 371}{5}

5^{7} \cdot 2^{6} 371 = 5000000371

= \frac{5000000 371}{5}

Factor

5000000 : 5^{7} \cdot 2^{6}

= \frac{5 ^{7} \cdot 2 ^{6} 371}{5}

Cancel

\frac{2 ^{6} \cdot 5 ^{7} 371}{5} : 2^{6} \cdot 5^{\frac{13}{2}} 371

= 2^{6} \cdot 5^{\frac{13}{2}} 371

5^{\frac{13}{2}} = 5^{6} 5

= 2^{6} \cdot 5^{6} 5371

Apply radical rule:

a b = a \cdot b

5371 = 5 \cdot 371

= 2^{6} \cdot 5^{6} 5 \cdot 371

Multiply the numbers:

5 \cdot 371 = 1855

= 2^{6} \cdot 5^{6} 1855

2^{6} = 64

= 5^{6} \cdot 641855

5^{6} = 15625

= 64 \cdot 156251855

Multiply the numbers:

64 \cdot 15625 = 1000000

= 10000001855

600 \frac{2}{3}

32 + 325

(x + 6)^{4}

- \frac{1}{2} \times 5

\frac{x}{x ^{2} - 2 x}

What is 10^8*(sqrt(371))/(20sqrt(5)) ?
The solution to 10^8*(sqrt(371))/(20sqrt(5)) is 1000000sqrt(1855)