Explanation:
Right angled triangle=>$AB^{2}+BC^{2}=AC^{2}$
=>$5^{2}+5^{2}=(5\sqrt{2})^{2}$
=>25+25=$25\times 2$
=>50=50

Explanation:
solve it from right to left=$\sqrt{81}=9 then add with \sqrt{7}=>we get,\sqrt{9+7}=>\sqrt{16}$=4
then $\sqrt{4+60}=>\sqrt{64}=8$
then $\sqrt{8+248}=\sqrt{256}=16$
then $\sqrt{16+609}=\sqrt{625}=25$

Explanation:
the price of house decreased from 15,00,000 to 12,00,000
so there difference =15,00,000-12,00,000=3,00,000=3 lakhs
the decreased percentage(%)=$\dfrac{3}{15}\times100$
=20%

Explanation:
3(t-3)=5(2t+1)
3t-9=10t+5
7t=-14
t=$\dfrac{-14}{7}$
t=-2

Explanation:
the given question is in format of =$\dfrac{(a+b)^{2}}{a^{2}-b^{2}}$
therefore,=$\dfrac{(a+b)\times (a+b)}{(a+b) (a-b)}$
=$\dfrac{(a+b)}{(a-b)}$
ie.,=$\dfrac{1.75+0.75}{1.75-0.75}$
=2.5/1=2.5

Explanation:
$16^{3}+7^{3}-23^{3}$ is in the format of=$a^{3}+b^{3}-c^{3}$
then first take$ a^{3}+b^{3}=>16^{3}+7^{3}$ $[(a+b)(a^{2}-ab+b^{2})]$
$=>(16+7)(16^{2}-16(7)+7^{2})$
$=>23(256-112+49)$
=>23(144+49)
=>23(193)
=>4439
$7^{3}$=12167
$16^{3}+7^{3}-23^{3}$=4439-12167=-7728

Explanation:
$1,1^{3},2,2^{3},3,3^{3},4 then 4^{3} $will come in series therefore,$4^{3}=64$

Explanation:
Sum of the angles of triangle=$180^{0}$
therefore,x-30+x-45+x+15=$180^{0}$
3x-60=$180^{0}$
3x=$240^{0}$
x=$240^{0}$/3
x=$80^{0}$

Explanation:
Principal=Rs.12,000
Rate of interest=10%
years=2years
SI=$\dfrac{P\times N\times R}{100}$
=$\dfrac{12,000\times 2\times 10 }{100}$
=$\dfrac{240000}{100}$
=2400
CI=$A=P(1+\dfrac{r}{100})^ n-P$
$=12,000(1+\dfrac{10}{100})^2-12,000$
$=12,000(1+0.1)^2-12,000$
$=12,000(1.1)^2-12,000$
$=12,000\times 1.21-12,000$
$=14,520-12,000$
CI=Rs.2520
Diff btw CI and SI=2520-2400
=Rs.120