Evaluate

Problem

(9*(266178)−3986⋅403)/(√(,9*(407404)−15888196)√(,9*(22487)−162409))

Solution

1. Calculate the numerator by performing the multiplications and then the subtraction.

9⋅266178=2395602

3986⋅403=1606358

2395602−1606358=789244

2. Evaluate the first radicand (the expression inside the first square root).

9⋅407404=3666636

3666636−15888196=−12221560

3. Evaluate the second radicand (the expression inside the second square root).

9⋅22487=202383

202383−162409=39974

4. Identify that the first radicand is negative, which means the square root results in an imaginary number.

√(,−12221560)=i√(,12221560)

5. Simplify the denominator by multiplying the two square roots.

√(,−12221560)⋅√(,39974)=√(,−12221560⋅39974)

−12221560⋅39974=−488544639440

6. Divide the numerator by the simplified denominator.

789244/√(,−488544639440)=789244/(i√(,488544639440))

7. Rationalize the denominator by multiplying the numerator and denominator by i

(789244*i)/(−√(,488544639440))

8. Approximate the numerical value for clarity.

√(,488544639440)≈698959.68

789244/698959.68≈1.12917

Final Answer

(9*(266178)−3986⋅403)/(√(,9*(407404)−15888196)√(,9*(22487)−162409))=−789244/√(,488544639440)*i

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