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the product of the square of a number and the cube of the same number is equal to 243. find the number​

User Gin
by
3.4k points

2 Answers

4 votes

Answer:

The number is 3.

Explanation:

Let "The square of the number" be x^2.

Let "the cube of the same number" be x^3.

"product" means multiplication.

x^2 • x^3 = 243

Multiply. To multiply, add the exponents.

x^5 = 243

Take the 5th root of both sides. You can do this on many scientific calculators with a x^y button. Or raise 243^ (1/5)

1/5 power is the same as 5th root.

You might do it in your head by thinking "what number to the 5th power is 243"

x = 3

Check 3^5 = 243

also

3^2 • 3^3 = 43

9 • 27 = 243

243 = 243 check

User BjornS
by
3.7k points
12 votes

Answer:

x=3

Explanation:

X^2*x^3 → x^5

x^5 = 243 means x = 3

User Txulu
by
3.5k points