1) [tex]\( 3^2 + 8^2 = 73 \)[/tex]

2) [tex]\( 22^2 - 20^2 = \square \)[/tex]

3) [tex]\( 7^2 + 5^2 = 64 \)[/tex]

4) [tex]\( 9^2 - 5^2 = 56 \)[/tex]

5) [tex]\( 10^2 - 8^2 = \square \)[/tex]

6) [tex]\( 9^2 - 8^2 = \square \)[/tex]

7) [tex]\( \frac{13^2 - 5^2}{24} = \square \)[/tex]

8) [tex]\( 8^2 - 7^2 = \square \)[/tex]

9) [tex]\( \sqrt{5^2 - 3^2} = \square \)[/tex]

10) [tex]\( 7^2 - 3^3 = \square \)[/tex]



Answer :

Sure! Let's solve each of the given mathematical problems step-by-step.

For the expressions where the value is given, let's confirm them first:

1) [tex]\(3^2 + 8^2 = 9 + 64 = 73\)[/tex] (Given)

3) [tex]\(7^2 + 5^2 = 49 + 25 = 74\)[/tex] (It was given as 64, but the correct answer is 74)

4) [tex]\(9^2 - 5^2 = 81 - 25 = 56\)[/tex] (Given)

Now, let's solve the others step-by-step to confirm the results:

2) [tex]\(22^2 - 20^2\)[/tex]

Using the formula for the difference of squares:

[tex]\[ a^2 - b^2 = (a + b)(a - b) \][/tex]

[tex]\[ 22^2 - 20^2 = (22 + 20)(22 - 20) = 42 \times 2 = 84 \][/tex]

Hence, [tex]\(22^2 - 20^2 = 84\)[/tex].

5) [tex]\(10^2 - 8^2\)[/tex]

Using the difference of squares formula:

[tex]\[ 10^2 - 8^2 = (10 + 8)(10 - 8) = 18 \times 2 = 36 \][/tex]

Hence, [tex]\(10^2 - 8^2 = 36\)[/tex].

6) [tex]\(9^2 - 8^2\)[/tex]

Using the difference of squares formula:

[tex]\[ 9^2 - 8^2 = (9 + 8)(9 - 8) = 17 \times 1 = 17 \][/tex]

Hence, [tex]\(9^2 - 8^2 = 17\)[/tex].

7) [tex]\(\frac{13^2 - 5^2}{24}\)[/tex]

Solving inside the fraction first:

[tex]\[ 13^2 - 5^2 = 169 - 25 = 144 \][/tex]

Then, divide by 24:

[tex]\[ \frac{144}{24} = 6 \][/tex]

Hence, [tex]\(\frac{13^2 - 5^2}{24} = 6\)[/tex].

8) [tex]\(8^2 - 7^2\)[/tex]

Using the difference of squares formula:

[tex]\[ 8^2 - 7^2 = (8 + 7)(8 - 7) = 15 \times 1 = 15 \][/tex]

Hence, [tex]\(8^2 - 7^2 = 15\)[/tex].

9) [tex]\(\sqrt{5^2 - 3^2}\)[/tex]

Solving inside the square root first:

[tex]\[ 5^2 - 3^2 = 25 - 9 = 16 \][/tex]

Then, take the square root:

[tex]\[ \sqrt{16} = 4 \][/tex]

Hence, [tex]\(\sqrt{5^2 - 3^2} = 4\)[/tex].

10) [tex]\(7^2 - 3^3\)[/tex]

First, calculate each term:

[tex]\[ 7^2 = 49 \][/tex]

[tex]\[ 3^3 = 27 \][/tex]

Then, subtract them:

[tex]\[ 49 - 27 = 22 \][/tex]

Hence, [tex]\(7^2 - 3^3 = 22\)[/tex].

So, here are the values for each:

2) [tex]\(22^2 - 20^2 = 84\)[/tex]
5) [tex]\(10^2 - 8^2 = 36\)[/tex]
7) [tex]\(\frac{13^2 - 5^2}{24} = 6\)[/tex]
8) [tex]\(8^2 - 7^2 = 15\)[/tex]
9) [tex]\(\sqrt{5^2 - 3^2} = 4\)[/tex]
10) [tex]\(7^2 - 3^3 = 22\)[/tex]