Find the sum of the first 8 multiples of 3- Maths Q-A

Compute the required value:The prime factorization of 324 is 2× 2× 3× 3× 3× 3.⇒√(324)=√(2× 2× 3× 3× 3× 3)0ex0ex⇒√(324)=√(2^2×3^2×3^2)0ex0ex⇒√(324)=2× 3× 30ex0ex ...

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Byju's Answer

Standard XIII

Mathematics

Finding Integral Part of Numbers of the Form a^b Where a Is Irrational

Find the sum ...

Question

Find the square root of $324$ .

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Solution

Compute the required value:
The prime factorization of $324$ is $2 \times 2 \times 3 \times 3 \times 3 \times 3$ .
$\Rightarrow \sqrt{324} = \sqrt{2 \times 2 \times 3 \times 3 \times 3 \times 3} \Rightarrow \sqrt{324} = \sqrt{2^{2} \times 3^{2} \times 3^{2}} \Rightarrow \sqrt{324} = 2 \times 3 \times 3 = 18$
Hence, the square root of $324$ is $18$ .

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Question 133

Solve the following question:

Find the square root of 324 by the method of repeated subtraction.

Q. Write the following numbers in the form of rational indices.
(1) Square root of 5th power of 121
(2) Cube of 4th root of 324
(3) 5th root of square of 264
(4) Cube of cube root of 3

Find the square root of:

$(i) \frac{441}{961}$ $(i i) \frac{324}{841}$ $(i i i) 4 \frac{29}{49}$ $(i v) 2 \frac{14}{25}$ $(v) 2 \frac{137}{196}$

$(v i) 23 \frac{26}{121}$ $(v i i) 25 \frac{544}{729}$ $(v i i i) 75 \frac{46}{49}$ $(i x) 3 \frac{942}{2209}$ $(x) 3 \frac{334}{3025}$

$(x i) 21 \frac{2797}{3364}$ $(x i i) 38 \frac{11}{25}$ $(x i i i) 23 \frac{394}{729}$ $(x i v) 21 \frac{51}{169}$ $(x v) 10 \frac{151}{169}$

Q. Write the square roots of each of the following numbers:

(1) 9
(2) 25
(3) 100
(4) 196
(5) 324
(6) 576

Q. Find the square root of

324

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Find the square root of 324.

Compute the required value:The prime factorization of 324 is 2×2×3×3×3×3.⇒324=2×2×3×3×3×3⇒324=22×32×32⇒324=2×3×3=18Hence, the square root of 324 is 18.

Find the square root of $324$ .