Identify the pattern. The given numbers are 1^2=1, 2^2=4, 3^2=9.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the problems:
4. Find the next six square numbers in this pattern: 1; 4; 9.
Step 1: Identify the pattern. The given numbers are $1^2=1$, $2^2=4$, $3^2=9$.
Step 2: Calculate the next six square numbers.
$4^2 = 16$
$5^2 = 25$
$6^2 = 36$
$7^2 = 49$
$8^2 = 64$
$9^2 = 81$
The next six square numbers are $\boxed{16, 25, 36, 49, 64, 81}$.
5. Calculate:
a)
Step 1: Calculate the square.
$$5^2 = 5 \times 5 = \boxed{25}$$
b)
Step 1: Calculate the square.
$$8^2 = 8 \times 8 = \boxed{64}$$
d)
Step 1: Calculate the square.
$$10^2 = 10 \times 10 = \boxed{100}$$
e)
Step 1: Calculate the square.
$$11^2 = 11 \times 11 = \boxed{121}$$
6. Compare these calculations. Fill in $>$; $<$; $=$.
a)
Step 1: Calculate both sides.
$2^2 = 2 \times 2 = 4$
$2 \times 2 = 4$
Step 2: Compare the results.
$4 = 4$
So, $2^2 \boxed{=} 2 \times 2$.
b)
Step 1: Calculate both sides.
$5^2 = 5 \times 5 = 25$
$5 \times 2 = 10$
Step 2: Compare the results.
$25 > 10$
So, $5^2 \boxed{>} 5 \times 2$.
d)
Step 1: Calculate both sides.
$9^2 = 9 \times 9 = 81$
$9 \times 2 = 18$
Step 2: Compare the results.
$81 > 18$
So, $9^2 \boxed{>} 9 \times 2$.
e)
Step 1: Calculate both sides.
$11 \times 11 = 121$
$11^2 = 11 \times 11 = 121$
Step 2: Compare the results.
$121 = 121$
So, $11 \times 11 \boxed{=} 11^2$.
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