What is expand sqrt((1+21t)^2+(1+21t)^2) ?

The solution to expand sqrt((1+21t)^2+(1+21t)^2) is 21sqrt(2)t+sqrt(2)

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expand sqrt((1+21t)^2+(1+21t)^2)

expand

(1 + 21 t)^{2} + (1 + 21 t)^{2}

212 t + 2

Solution steps

(1 + 21 t)^{2} + (1 + 21 t)^{2}

Add similar elements:

(21 t + 1)^{2} + (21 t + 1)^{2} = 2 (21 t + 1)^{2}

= 2 (21 t + 1)^{2}

(1 + 21 t)^{2} = 1 + 42 t + 441 t^{2}

= 2 (441 t^{2} + 42 t + 1)

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 2 441 t^{2} + 42 t + 1

Factor

441 t^{2} + 42 t + 1 : (21 t + 1)^{2}

= 2 (21 t + 1)^{2}

Apply radical rule:

assuming

a \geq 0

(21 t + 1)^{2} = 21 t + 1

= 2 (21 t + 1)

Apply the distributive law:

a (b + c) = ab + a c

a = 2, b = 21 t, c = 1

= 2 \cdot 21 t + 2 \cdot 1

= 212 t + 1 \cdot 2

Multiply:

1 \cdot 2 = 2

= 212 t + 2

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What is expand sqrt((1+21t)^2+(1+21t)^2) ?
The solution to expand sqrt((1+21t)^2+(1+21t)^2) is 21sqrt(2)t+sqrt(2)