Question

27 корень[321] - 15 корень[105]

Answer 1

$27\sqrt{321}-15\sqrt{105}=27\sqrt{3*107}-15\sqrt{3*35}=27\sqrt{3}*\sqrt{107} -15\sqrt{3}*\sqrt{35} =3\sqrt{3}(9\sqrt{107}-5\sqrt{35})$

Answer 2

27 $\sqrt{321} - 15\sqrt{105} = 3 (9\sqrt{321} -5\sqrt{105)}$

Answer 3

To evaluate this expression, we can use a calculator or simplify it by expressing the numbers under the square roots as products of their prime factors:

321 = 3 × 107 105 = 3 × 5 × 7

Then we can apply the rules of square roots:

√321 = √(3 × 107) = √3 × √107 √105 = √(3 × 5 × 7) = √3 × √5 × √7

Substituting these expressions into the original equation, we get:

27√3 × √107 - 15√3 × √5 × √7

Next, we can simplify further by factoring out the common factor of √3:

√3(27√107 - 15√5 × √7)

Finally, we can use a calculator to evaluate the numerical values of the square roots and perform the arithmetic:

√107 ≈ 10.344 √5 ≈ 2.236 √7 ≈ 2.646

Substituting these values, we get:

√3(27 × 10.344 - 15 × 2.236 × 2.646) ≈ 81.33

Therefore, the value of the expression 27√321 - 15√105 is approximately 81.33.