Step 1: Identify the form of the expression. The expression is in the form (a−b)², where a = 3√(5) and b = 4√(3). The formula for (a−b)² is a² − 2ab + b². Step 2: Calculate a². a² = (3√(5))² = 3² × (√(5))² = 9 × 5 = 45 Step 3: Calculate b². b² = (4√(3))² = 4² × (√(3))² = 16 × 3 = 48 Step 4: Calculate 2ab. 2ab = 2 × (3√(5)) × (4√(3)) = 2 × 3 × 4 × √(5 × 3) = 24√(15) Step 5: Substitute the calculated values into the formula. (3√(5) − 4√(3))² = a² − 2ab + b² = 45 − 24√(15) + 48 Step 6: Combine the constant terms. 45 − 24√(15) + 48 = (45 + 48) − 24√(15) = 93 − 24√(15) The simplified expression is: 93 − 24√(15)

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(3√5 - 4√3)²

September 29, 2026Mathematics

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Answer

93 - 24\sqrt{15}

Step-by-step solution

6 steps

Identify the form of the expression.
The expression is in the form $(a-b)^2$ , where $a = 3\sqrt{5}$ and $b = 4\sqrt{3}$ .
The formula for $(a-b)^2$ is $a^2 - 2ab + b^2$ .
Calculate $a^2$ .
$a^2 = (3\sqrt{5})^2 = 3^2 \times (\sqrt{5})^2 = 9 \times 5 = 45$
Calculate $b^2$ .
$b^2 = (4\sqrt{3})^2 = 4^2 \times (\sqrt{3})^2 = 16 \times 3 = 48$
Calculate $2ab$.
$2ab = 2 \times (3\sqrt{5}) \times (4\sqrt{3}) = 2 \times 3 \times 4 \times \sqrt{5 \times 3} = 24\sqrt{15}$
Substitute the calculated values into the formula.
$(3\sqrt{5} - 4\sqrt{3})^2 = a^2 - 2ab + b^2 = 45 - 24\sqrt{15} + 48$
Combine the constant terms.
$45 - 24\sqrt{15} + 48 = (45 + 48) - 24\sqrt{15} = 93 - 24\sqrt{15}$
The simplified expression is:
$93 - 24\sqrt{15}$

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(3√5 - 4√3)²

Answer

Step-by-step solution

Identify the form of the expression.

Calculate a2a^2a2.

Calculate b2b^2b2.

Calculate $2ab$.

Substitute the calculated values into the formula.

Combine the constant terms.

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