We read your photo as:

To simplify the expression, rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator. The conjugate of sqrt(7) + sqrt(2) is $sqrt(7) - sqrt(2)

Languages

ScanSolve AI Answer

Answer

7−25\frac{\sqrt{7} - \sqrt{2}}{5}

Step-by-step solution

4 steps

  1. To simplify the expression, rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator.

    The conjugate of 7+2\sqrt{7} + \sqrt{2} is 7−2\sqrt{7} - \sqrt{2}.

    17+2×7−27−2\frac{1}{\sqrt{7} + \sqrt{2}} \times \frac{\sqrt{7} - \sqrt{2}}{\sqrt{7} - \sqrt{2}}

  2. Multiply the numerators.

    1×(7−2)=7−21 \times (\sqrt{7} - \sqrt{2}) = \sqrt{7} - \sqrt{2}

  3. Multiply the denominators using the difference of squares formula (a+b)(a−b)=a2−b2(a+b)(a-b) = a^2 - b^2.

    (7+2)(7−2)=(7)2−(2)2(\sqrt{7} + \sqrt{2})(\sqrt{7} - \sqrt{2}) = (\sqrt{7})^2 - (\sqrt{2})^2 =7−2= 7 - 2 =5= 5

  4. Combine the simplified numerator and denominator.

    7−25\frac{\sqrt{7} - \sqrt{2}}{5}
Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Languages Questions

QTo rationalize the denominator, multiply the numerator and denominator by the conjugate of the…QRationalize the denominator of the expression (1)/(sqrt(7)+2) and leave the answer in surd form.QRationalize the denominator. (i) 1 / sqrt(7) + sqrt(2) (ii) 3 / (2sqrt(5) − 3sqrt(2)) (iii) 4 / (7…QSimplify the expression: ((2+sqrt(7))/3) × ((2-sqrt(7))/3)QRationalize the denominator of the expression (3√2 − 4√3) / (4√3 − 2√2).
See all Languages questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.