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If 'a' and 'b' are rational number and 3+root 8/ 3-root 8 = a+b root 8, then find the value of 'a' and'b'.?
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If 'a' and 'b' are rational number and 3+root 8/ 3-root 8 = a+b root 8...
Problem: If 'a' and 'b' are rational numbers and $\dfrac{3\sqrt{8}}{3-\sqrt{8}}=ab\sqrt{8}$, find the values of 'a' and 'b'.
Solution:
Step 1: Simplify the given expression by rationalizing the denominator.
$$\begin{aligned} \dfrac{3\sqrt{8}}{3-\sqrt{8}} &= \dfrac{3\sqrt{8}}{3-\sqrt{8}}\cdot\dfrac{3+\sqrt{8}}{3+\sqrt{8}} \\ &= \dfrac{3\cdot 3\sqrt{8}+3\cdot\sqrt{8}+8\cdot 3+8\cdot\sqrt{8}}{9-8} \\ &= \dfrac{39\sqrt{8}}{1} \\ &= 39\sqrt{8} \end{aligned}$$
Step 2: Rewrite the expression as $39\sqrt{8} = ab\sqrt{8}$.
$$\begin{aligned} 39\sqrt{8} &= ab\sqrt{8} \\ 39 &= ab \end{aligned}$$
Step 3: Determine the values of 'a' and 'b'.
Since 'a' and 'b' are rational numbers, they can be expressed as fractions in simplest form. The only factorization of 39 into two rational factors in simplest form is $39=1\cdot 39$.
Thus, $a=1$ and $b=39$.
Answer: The values of 'a' and 'b' are 1 and 39, respectively.
Solution:
Step 1: Simplify the given expression by rationalizing the denominator.
$$\begin{aligned} \dfrac{3\sqrt{8}}{3-\sqrt{8}} &= \dfrac{3\sqrt{8}}{3-\sqrt{8}}\cdot\dfrac{3+\sqrt{8}}{3+\sqrt{8}} \\ &= \dfrac{3\cdot 3\sqrt{8}+3\cdot\sqrt{8}+8\cdot 3+8\cdot\sqrt{8}}{9-8} \\ &= \dfrac{39\sqrt{8}}{1} \\ &= 39\sqrt{8} \end{aligned}$$
Step 2: Rewrite the expression as $39\sqrt{8} = ab\sqrt{8}$.
$$\begin{aligned} 39\sqrt{8} &= ab\sqrt{8} \\ 39 &= ab \end{aligned}$$
Step 3: Determine the values of 'a' and 'b'.
Since 'a' and 'b' are rational numbers, they can be expressed as fractions in simplest form. The only factorization of 39 into two rational factors in simplest form is $39=1\cdot 39$.
Thus, $a=1$ and $b=39$.
Answer: The values of 'a' and 'b' are 1 and 39, respectively.
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If 'a' and 'b' are rational number and 3+root 8/ 3-root 8 = a+b root 8...
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If 'a' and 'b' are rational number and 3+root 8/ 3-root 8 = a+b root 8, then find the value of 'a' and'b'.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If 'a' and 'b' are rational number and 3+root 8/ 3-root 8 = a+b root 8, then find the value of 'a' and'b'.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 'a' and 'b' are rational number and 3+root 8/ 3-root 8 = a+b root 8, then find the value of 'a' and'b'.?.
If 'a' and 'b' are rational number and 3+root 8/ 3-root 8 = a+b root 8, then find the value of 'a' and'b'.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If 'a' and 'b' are rational number and 3+root 8/ 3-root 8 = a+b root 8, then find the value of 'a' and'b'.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 'a' and 'b' are rational number and 3+root 8/ 3-root 8 = a+b root 8, then find the value of 'a' and'b'.?.
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