Answer:
6. [tex]2\sqrt{2}[/tex]
7. [tex]7\sqrt{2}[/tex]
8. [tex]\sqrt{10}[/tex]
9. [tex]8\sqrt{2}[/tex]
10. [tex]3[/tex]
11. [tex]2\sqrt{5}[/tex]
Step-by-step explanation:
for all of these problems i used the pythagorean theorem, which is [tex]a^{2} + b^{2} = c^{2}[/tex]
6.
[tex]2^{2} + 2^{2} = c^{2}[/tex]
[tex]8=c^{2}[/tex]
[tex]\sqrt{8} =\sqrt{c^{2} }[/tex]
[tex]2\sqrt{2}[/tex]
7.
[tex]7^{2} + 7^{2} = c^{2}[/tex]
[tex]49+49=c^{2}[/tex]
[tex]98=c^{2}[/tex]
[tex]\sqrt{98} =\sqrt{c^{2} }[/tex]
[tex]7\sqrt{2}[/tex]
8.
[tex](\sqrt{5})^{2} +(\sqrt{5})^{2} =c^{2}[/tex]
[tex]5+5=c^{2}[/tex]
[tex]\sqrt{10}[/tex]
9.
[tex]8^{2} +8^{2} =c^{2}[/tex]
[tex]64+64=c^{2}[/tex]
[tex]128=c^{2}[/tex]
[tex]\sqrt{128} =\sqrt{c^{2} }[/tex]
[tex]8\sqrt{2}[/tex]
10.
[tex](\sqrt{3}) ^{2} + (\sqrt{3}) ^{2} = c^{2}[/tex]
[tex]3+3=c^{2}[/tex]
[tex]9=c^{2}[/tex]
[tex]\sqrt{9} =\sqrt{c^{2} }[/tex]
[tex]3[/tex]
11.
[tex](\sqrt{10}) ^{2} + (\sqrt{10}) ^{2} = c^{2}[/tex]
[tex]10+10=c^{2}[/tex]
[tex]20=c^{2}[/tex]
[tex]\sqrt{20} =\sqrt{c^{2} }[/tex]
[tex]2\sqrt{5}[/tex]
