1.03 Square roots of perfect squares
State whether the following numbers are perfect squares:
Explain how you know whether a number is a perfect square.
If u^{2} = d, what does the square root property state that u is equal to?
Evaluate the following:
For each of the following, determine the square root:
If 5 \times 5 = 25, find \sqrt{25}.
If 7 \times 7 = 49, find \sqrt{49}.
If 6 \times 6 = 36, find -\sqrt{36} .
If 7 \times 7 = 49, find -\sqrt{49}.
Evaluate the following:
\sqrt{169}
\sqrt{225}
-\sqrt{4}
-\sqrt{81}
-\sqrt{121}
-\sqrt{196}
Evaluate the following:
Harry was working out 2^{2} \times 5^{2} and thought that he could simplify the expression using the fact that 2 \times 5 = 10.
Evaluate 2^{2} \times 5^{2}, by first evaluating each square.
Now, using the fact 2 \times 5 = 10, evaluate 10^{2}.
Is 2^{2} \times 5^{2} = \left( 2 \times 5\right)^{2} a true statement?
Calculate 4^{2} \times 2^{2} using the above method.
For each of the following situations:
Ralph tried to evaluate the expression 2\left(3+2\right)^2. He thought that he had the right answer and submitted the following to his teacher 2\left(3+2\right)^2 = 2\left(5\right)^2 = 10^2 = 100.
Ida tried to evaluate the expression \sqrt{9}\left(8 \div 4 - 3 \times 4 + 4^2 + 3\right). She submitted the following to her teacher \sqrt{9}\left(8 \div 4 - 3 \times 4 + 4^2 + 3\right) = \sqrt{9}\left(2 -12 + 16 + 3\right) = \sqrt{9}\left(9\right) = \sqrt{81} = 9.
The equation x^{2} - 144 = 0 has a positive integer solution x = 12.
Find the negative integer that is also a solution.
Solve for each of the following equation for x: