What is the value of sqrt(9.8*tan(30)0.35) ?

The value of sqrt(9.8*tan(30)0.35) is (7sqrt(7)*3^{3/4})/(30)

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Popular Trigonometry >

sqrt(9.8*tan(30)0.35)

Solution

9.8 \cdot tan (3 0^{\circ}) 0.35

Solution

\frac{7 7 \cdot 3 ^{\frac{3}{4}}}{30}

Decimal

1.40723 \dots

Solution steps

9.8 tan (3 0^{\circ}) \cdot 0.35

= \frac{49}{5} tan (3 0^{\circ}) \frac{7}{20}

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

= \frac{49}{5} \cdot \frac{3}{3} \cdot \frac{7}{20}

Simplify

\frac{49}{5} \cdot \frac{3}{3} \cdot \frac{7}{20} : \frac{7 7 \cdot 3 ^{\frac{3}{4}}}{30}

\frac{49}{5} \cdot \frac{3}{3} \cdot \frac{7}{20}

Multiply

\frac{49}{5} \cdot \frac{3}{3} \cdot \frac{7}{20} : \frac{343}{100 3}

\frac{49}{5} \cdot \frac{3}{3} \cdot \frac{7}{20}

Multiply fractions:

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

= \frac{49 3 \cdot 7}{5 \cdot 3 \cdot 20}

Multiply the numbers:

49 \cdot 7 = 343

= \frac{343 3}{5 \cdot 3 \cdot 20}

Multiply the numbers:

5 \cdot 3 \cdot 20 = 300

= \frac{343 3}{300}

Factor

300 : 2^{2} \cdot 5^{2} \cdot 3

Factor

300 = 2^{2} \cdot 5^{2} \cdot 3

= \frac{343 3}{2 ^{2} \cdot 5 ^{2} \cdot 3}

Cancel

\frac{343 3}{2 ^{2} \cdot 3 \cdot 5 ^{2}} : \frac{343}{2 ^{2} 3 \cdot 5 ^{2}}

\frac{343 3}{2 ^{2} \cdot 3 \cdot 5 ^{2}}

Apply radical rule:

3 = 3^{\frac{1}{2}}

= \frac{343 \cdot 3 ^{\frac{1}{2}}}{2 ^{2} \cdot 5 ^{2} \cdot 3}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{3 ^{\frac{1}{2}}}{3 ^{1}} = \frac{1}{3 ^{1 - \frac{1}{2}}}

= \frac{343}{2 ^{2} \cdot 5 ^{2} \cdot 3 ^{- \frac{1}{2} + 1}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{343}{2 ^{2} \cdot 5 ^{2} \cdot 3 ^{\frac{1}{2}}}

Apply radical rule:

3^{\frac{1}{2}} = 3

= \frac{343}{2 ^{2} \cdot 5 ^{2} 3}

= \frac{343}{2 ^{2} 3 \cdot 5 ^{2}}

2^{2} 3 \cdot 5^{2} = 1003

2^{2} 3 \cdot 5^{2}

2^{2} = 4

= 5^{2} \cdot 43

5^{2} = 25

= 4 \cdot 253

Multiply the numbers:

4 \cdot 25 = 100

= 1003

= \frac{343}{100 3}

= \frac{343}{100 3}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{343}{100 3}

Apply radical rule:

assuming

a \geq 0, b \geq 0

1003 = 1003

= \frac{343}{100 3}

343 = 77

343

Prime factorization of

343 : 7^{3}

343

343

divides by

7343 = 49 \cdot 7

= 7 \cdot 49

49

divides by

749 = 7 \cdot 7

= 7 \cdot 7 \cdot 7

7

is a prime number, therefore no further factorization is possible

= 7 \cdot 7 \cdot 7

= 7^{3}

= 7^{3}

Apply exponent rule:

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

= 7^{2} \cdot 7

Apply radical rule:

= 7 7^{2}

Apply radical rule:

7^{2} = 7

= 77

= \frac{7 7}{100 3}

100 = 10

100

Factor the number:

100 = 1 0^{2}

= 1 0^{2}

Apply radical rule:

1 0^{2} = 10

= 10

= \frac{7 7}{10 3}

Apply radical rule:

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

= (3^{\frac{1}{2}})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot \frac{1}{2}}

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

\frac{1}{2} \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 1}{2 \cdot 2}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{1}{4}

= 3^{\frac{1}{4}}

Rationalize

Multiply by the conjugate

\frac{3 ^{\frac{3}{4}}}{3 ^{\frac{3}{4}}}

Apply exponent rule:

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

= 10 \cdot 3^{\frac{3}{4} + \frac{1}{4}}

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

3^{\frac{3}{4} + \frac{1}{4}}

Combine the fractions

\frac{3}{4} + \frac{1}{4} : 1

Apply rule

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

= \frac{3 + 1}{4}

Add the numbers:

3 + 1 = 4

= \frac{4}{4}

Apply rule

\frac{a}{a} = 1

= 1

= 3^{1}

Apply rule

a^{1} = a

= 3

= 10 \cdot 3

Multiply the numbers:

10 \cdot 3 = 30

= 30

= \frac{7 7 \cdot 3 ^{\frac{3}{4}}}{30}

= \frac{7 7 \cdot 3 ^{\frac{3}{4}}}{30}

= \frac{7 7 \cdot 3 ^{\frac{3}{4}}}{30}

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Frequently Asked Questions (FAQ)

What is the value of sqrt(9.8*tan(30)0.35) ?
The value of sqrt(9.8*tan(30)0.35) is (7sqrt(7)*3^{3/4})/(30)