Question

Find the smallest positive number from the numbers below

• A. $10-3\sqrt{11}$
• B. $3\sqrt{11}-10$
• C. $51-10\sqrt{26}$
• D. $18-5\sqrt{13}$

Answer 1

Answer: (C)

$51-10\sqrt{26}$

(a) Value of $\sqrt{11}$ is $3.317$, therefore, we have

$10-3\sqrt{11}=10-(3\times 3.317)=10-9.951=0.049$

Thus, $10-3\sqrt{11}=0.049$ which is a positive integer.

(b) Value of $\sqrt{11}$ is $3.317$, therefore, we have

$3\sqrt{11}-10=(3\times 3.317)-10=9.951-10=-0.049$

Thus, $3\sqrt{11}-10=-0.049$ which is a negative integer.

(c) Value of $\sqrt{26}$ is $5.099$, therefore, we have

$51-10\sqrt{26}=51-(10\times 5.099)=51-50.99=0.01$

Thus, $51-10\sqrt{26}=0.01$which is a positive integer.

(d) Value of $\sqrt{13}$ is $3.605$, therefore, we have

$18-5\sqrt{13}=18-(5\times 3.605)=18-18.025=-0.025$

Thus, $18-5\sqrt{13}=-0.025$which is a negative integer.

Therefore, we conclude that $0.01$ is the smallest positive integer amongst all because $51-10\sqrt{26}=0.01$.

Hence, the smallest positive number is $51-10\sqrt{26}$