Question

1) How would you divide the expression \(\frac{36-27c}{9}\)?

a) \(\frac{4-3c}{1}\)
b) \(\frac{4-3c}{9}\)
c) \(\frac{36-27c}{9}\)
d) \(\frac{36-27c}{1}\)

2) What is a square root and how is it different from dividing?
a) A square root is the result of dividing a number by itself.
b) A square root is the result of multiplying a number by itself.
c) A square root is the result of adding a number to itself.
d) A square root is the result of subtracting a number from itself.

3) Simplify the square root \(\sqrt{50}\) by dividing out the perfect square.
a) \(\sqrt{5}\)
b) \(\sqrt{10}\)
c) \(\sqrt{25}\)
d) \(\sqrt{50}\)

Answer 1

1) The expression
`\((36-27c)/(9)\)` simplifies to
`\((4-3c)/(1)\),` making option a) the correct choice. 2) A square root is the result of finding a number that, when multiplied by itself, equals the given number;
`\(√(50)\)` simplifies to
`\(5√(2)\),`so the correct choice is b)
`\(√(10)\)`.

Step-by-step explanation:

1) To divide the expression
`\((36-27c)/(9)\)`, we can simplify both the numerator and the denominator. Dividing each term in the numerator by 9 yields
`\((4-3c)/(1)\)`, making option a) the correct choice.

2) A square root is denoted by
`\(√(x)\)` and represents the principal (non-negative) square root of x. It is the value that, when multiplied by itself, equals x. This is distinct from division, where we find the quotient or the result of dividing one number by another.

3) To simplify
`\(√(50)\)`, we factorize 50 into
`\(25 * 2\)`. Taking the square root of 25 yields 5, and we are left with
`\(√(2)\)`, resulting in
`\(5√(2)\)`. Therefore, the correct choice is b)
`\(√(10)\)`.