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How do you simplify 500720?

Answer
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Hint: We write the prime factorization of the numbers inside the square root and try to pair and make squares of values such that we are able to cancel the square root by square power.
Prime factorization is a process of writing a number in multiple of its factors where all factors are prime numbers.
Law of exponent states that when the base is same is same in division we can subtract the powers i.e. pmpn=pmn

Complete step-by-step answer:
We have to simplify the value of 500720 … (1)
We will write the prime factorization of the numbers 500 and 720
500=2×2×5×5×5
720=2×2×2×2×3×3×5
Since we know the law of exponents so we can collect the powers of same base
500=22×53
720=24×32×51
Now we substitute the value of 500 and 720 back in equation (1)
500720=22×5324×32×51
500720=2224×5351×132
We can write 1=30to make the base the same for division.
We now use the rule of exponents that when the base is same in division we subtract the powers i.e. pmpn=pmn
500720=224×531×302
Calculate the powers
500720=22×52×32
Write all powers with negative sign in denominator as we know x1=1x
500720=5222×32
Since the powers in the denominator are same we can multiply the bases i.e. pm×qm=(p×q)m
500720=52(2×3)2
500720=5262
Now we know that we can pair the terms using the rule a2b2=(ab)2in right hand side of the equation
500720=(56)2
We can cancel the square root by square power in right hand side of the equation
500720=56
The value of 500720=is 56.

We can further divide 5 by 6 and write the answer as 0.83333333.

Note:
Many students make the mistake of calculating the division inside the square root which will be a long decimal value and then use a long division method to calculate its square root. Keep in mind if we know the square values of the first few natural numbers we can directly write the values of square root as natural numbers be it in division and then after removing square root we divide the values.
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