Question

finde the cube root without finding prime factoe of 1)157464

2)5832
3)19683
4)13824​

Answer 1

Answer:

1. Seperate 157464 in two parts

(157) (464)

Take Ist part= 464

Digit on unit place= 4

Cube of 4= 4*4*4=64

Take only unit digit=4

Now take second part=157

157 lies in 5^3 to 6^3

For example..... 157 lies in (125 to 216)

take 5 for tens place

So the number will be 54

Check.......54*54*54=157464

2. Take L C M of 5832

Take the L C M from 2

when you take L C M come 6,2

And write like this 2*2*2--2*2*2

than take both sides 2

and write like this 2*2

and multiple both the 2

and answer is 4

3. 19683 = {3×3×3}×{3×3×3}×{3×3×3}

19683 = 27×27×27

4. 13824= 2*2*2*2*2*2*2*2*2*3*3*3

2*2*2*3= 24

Answer 2

Step-by-step explanation:

❥ Estimation Method.

❥By this method we can find cube root of any number without finding prime factors.

$\huge\tt{solution}$

1. 157464

• Seperate 157464 in two parts

(157) (464)

• Take Ist part= 464

• Digit on unit place= 4

• Cube of
• $4 \times 4 \times 4 = 64$
• Take only unit digit=4

• Now take second part=157

• 157 lies in
• ${5}^{3}$

to

${6}^{3}$

• For example..... 157 lies in (125 to 216)

• take 5 for tens place

• So the number will be 54

Check-

$54 \times 54 \times 54 = 157464$

2. 5832

• Seperate 5832 in two parts

(5) (832)

• Take first part - (832)
• Digit on unit place - 2
• Cube of 2-
• $2 \times 2 \times 2 = 8$
• Now take second part -5
• 5 is the only digit.
• Lies between
• ${1}^{3}$and
• ${2}^{3}$
• Number we take will be 18.

Check-

$18 \times 18 \times 18 = 5832$

3. 19683

• Seperate 19683 in two parts

(19) (683)

• Take first part-683
• Digit on unit place-3
• Cube of 3-
• $3 \times 3 \times 3 = 27$
• Now take second part-(19)
• 19 lies between
• ${2}^{3}$and
• ${3}^{3}$
• Number we take will be 27.

Check- 27 \times 27 \times 27 = 19683