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Last updated on November 30th, 2024
The cube root of 1331 is the value which, when multiplied by itself three times (cubed), gives the original number 1331. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, designing structures, density and mass, used in day-to-day mathematics like exponents, etc.
The cube root of 1331 is 11. The cube root of 1331 is expressed as β1331 in radical form, where the β β β sign" is called the βradicalβ sign. In exponential form, it is written as (1331)1/3. If βmβ is the cube root of 1331, then, m3=1331. Let us find the value of βmβ.
The cube root of 1331 can be found through various methods like:
The steps involved to find β1331 are
1331 = 11Γ11Γ11
β1331 = β(11Γ11Γ11)
Here, for 1331, no remaining factors are there. We get one group of prime factor 11, i.e., (11Γ11Γ11).
So, 1331 is a Perfect cube. β1331=11.
The subtraction method involves subtracting successive odd numbers repeatedly.
Subtract the list of odd numbers β 1,7,19,37,61,91,127,169,217,271,331,397β¦β¦..successively till we get a zero.
Step 1 β Subtract the 1st odd number : 1331β1 = 1330
Step 2 β Subtract the next odd number: 1330β7 = 1323
Step 3 β Subtract the next odd number: 1323β19 = 1304
Step 4 β Subtract the next odd number: 1304β37 = 1267
Step 5 β Subtract the next odd number: 1267-61 = 1206
Step 6 β Subtract the next odd number: 1206-91 = 1115
Step 7 β Subtract the next odd number: 1115-127 = 988
Step 8 β Subtract the next odd number: 988-169 = 819
Step 9 β Subtract the next odd number: 819-217 = 602
Step 10 β Subtract the next odd number: 602-271=331
Step 11 β Subtract the next odd number: 331-331=0
Here, the subtraction took place 11 times to reach zero.
Hence, the cube root of 1331 is 11.
Misconceptions or mistakes are common, so let us see how we can avoid those from happening. Here are some misconceptions listed below with their respective solutions.
Find ((β343/ β1331) Γ (β512/ β1331))
((β343/ β1331) Γ (β512/ β1331))
=(7/ 11)Γ (8/ 11)
=56/121
Answer: 56/121
Simplified the expression and found the answer.
The length, breadth, and height of a cuboid is 9 units, 4 units, and 5 cm respectively. To find its volume, also find the measure of a side of a cube, whose volume is 1331 cubic units.
Volume of a cuboid = length Γ breadth Γ height = 9 Γ 4 Γ 5 cubic units = 180 cubic units.
Given, Volume of a cube = 1331 cubic units
β side Γ side Γ side = 1331 cubic units
β side = β1331
β side = 11 units
Answer: Volume of the cuboid = 180 cubic units
Side length of the cube = 11 units
Applied the formula and concept of the volume of a cuboid and cube and solved.
Multiply β1331 / β216
β1331/β216
= 11/6
Answer: 11/6
We know that the cubic root of 216 is 6, hence dividing β1331 by β216.
What is β(1331)βΆ* 1/6 ?
β(13316Γ1/6)
= (1331)1/3
= 11
Answer: 11
We solved and simplified the exponent part first using the fact that, (13316Γ1/6)=1331, then solved.
Find β(1000-(-331)).
β(1000-(-331))
= β(1000+331)
=β1331
=11
Answer: 11
Simplified the expression, and found out the cubic root of the result.
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.