Solve sqrt{2^100-2^99-2^98}

$$\sqrt{ { 2 }^{ 100 } - { 2 }^{ 99 } - { 2 }^{ 98 } }$$

Evaluate

$$562949953421312$$

Solution Steps

Calculate 2 to the power of 100 and get 1267650600228229401496703205376.

$$\sqrt{1267650600228229401496703205376-2^{99}-2^{98}}$$

Calculate 2 to the power of 99 and get 633825300114114700748351602688.

$$\sqrt{1267650600228229401496703205376-633825300114114700748351602688-2^{98}}$$

Subtract 633825300114114700748351602688 from 1267650600228229401496703205376 to get 633825300114114700748351602688.

$$\sqrt{633825300114114700748351602688-2^{98}}$$

Calculate 2 to the power of 98 and get 316912650057057350374175801344.

$$\sqrt{633825300114114700748351602688-316912650057057350374175801344}$$

Subtract 316912650057057350374175801344 from 633825300114114700748351602688 to get 316912650057057350374175801344.

$$\sqrt{316912650057057350374175801344}$$

Calculate the square root of 316912650057057350374175801344 and get 562949953421312.

$$562949953421312$$

Factor

$$2^{49}$$